Dtyjlui

Reinstall the GRUB boot loader to your Ubuntu installation in EFI mode this way ...

Boot from the Ubuntu installation medium and select 'Try Ubuntu without installing'.

(Boot your install medium in EFI mode, select the Ubuntu entry with UEFI in front.)

Once you are on the Live desktop, open a terminal and execute these commands :

sudo mount /dev/sdXXX /mnt

sudo mount /dev/sdXX /mnt/boot/efi

for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done

sudo chroot /mnt

grub-install /dev/sdX

update-grub  

Note : sdX = disk | sdXX = efi partition | sdXXX = system partition

To identify the partitions use GParted, the tool is included in the installation medium.

After having run the commands GRUB will be installed in the separate EFI partition.

Thanks to @cl-netbox for the instructions!

After I upgraded (Linux Mint 18.2 Sonya to 18.3 Sylvia) my system wouldn't boot so I followed the instructions above but still no success. I noticed however that my machine has /boot in a separate partition (possibly because I am using LVM) so my slightly modified process was:

sudo mount /dev/sdXXX /mnt

sudo mount /dev/sdXY /mnt/boot

sudo mount /dev/sdXX /mnt/boot/efi

for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done

sudo chroot /mnt

grub-install /dev/sdX

update-grub 

Note : sdX = disk | sdXX = efi partition | sdXY = boot partition | sdXXX = system partition

this is the only way that worked for me:
(System: sdb8, boot: sdb6, efi: sdb2)

sudo mount /dev/sdb8 /mnt 

sudo mount /dev/sdb6 /mnt/boot 

sudo mount /dev/sdb2 /mnt/boot/efi



sudo mount --bind /dev /mnt/dev &&

sudo mount --bind /dev/pts /mnt/dev/pts &&

sudo mount --bind /proc /mnt/proc &&

sudo mount --bind /sys /mnt/sys



sudo chroot /mnt



grub-install --target=x86_64-efi /dev/sdb



grub-install --recheck /dev/sdb



exit &&

sudo umount /mnt/sys &&

sudo umount /mnt/proc &&

sudo umount /mnt/dev/pts &&

sudo umount /mnt/dev &&

sudo umount /mnt

in addition to ci-netbox answer.

If your pendrive OS version does not match the one that is installed on the disk, grub-install may have difficulties to identify the right grub installation:

$ sudo chroot /mnt

# grub-install /dev/sdX

grub-install: error: /usr/lib/grub/i386-pc/modinfo.sh doesn't exist. 

Please specify --target or --directory.

Try to identify manually the installation to use

# ls /usr/lib/grub/

grub-mkconfig_lib  x86_64-efi  x86_64-efi-signed

Then restart grub-install :

# grub-install --target=x86_64-efi /dev/sdX 

Installing for x86_64-efi platform.

Installation finished. No error reported.

If you happen to lose the EFI partition, it's easy to get it back. You can use fdisk or parted to create a new GPT partition with type "EFI partition (1)" and format it with:

sudo mkfs.msdos /dev/sdX

then mount it and you can follow run:

sudo grub-install /dev/sdX

as in other solutions.

Also, if booting from live cd to recover it might happen that you are missing grub-efi-amd64-bin package and then line

"grub-install --target=x86_64-efi /dev/sdb" 

fails with error message: "grub-install: error: /usr/lib/grub/x86_64-efi/modinfo.sh doesn't exist. Please specify --target or --directory."

In this case run this outside of chroot

sudo apt get grub-efi-amd64-bin

and then add /usr/lib/grub/x86_64-efi to chroot mounts.

BTW "/dev/sdb" param is obsolete and is being ignored.