Actually after multiple times restart, the window opened and i moved with the installation but after done with the partition settings and other stuffs , the actual installation starts and system just got hanged in the middle, like this
I would use GParted from the live ISO to remove all partitions from the VirtualBox drive and try again.
There may be a setting you made in VirtualBox that Parrot doesn’t like. Did not make the guest hard drive dynamic or fixed size? You could open the *.vbox file in a text editor and post it here. Though I’m more familiar with using VMware and KVM virtual machines.
By any chance did you check the checksum of the iso you downloaded? There are a number of free utilities in Windows/Mac/Linux to create a checksum hash of your downloaded ISO which can be compared to the signed-hashes.txt to make sure the ISO isn’t corrupted.