sudo swapoff -a
First we must tell the system not to attempt to mount the swap partition on boot.
sudo scratch-text-editor /etc/fstab
Comment out (place a # before) or delete the line containing your swap partition which will be similar to this.
# swap was on /dev/sda3 during installation
UUID=3532d79f-8215-435b-b40e-36136e0e2a41 none swap sw 0 0
Then you can delete the swap partition with your partitioner of choice. Below is an example using GParted which can be installed via
sudo apt-get install gparted. Note that you will need to run the
swapoff command above (or select it from the GParted menu), before you can delete the partition.