I installed a Linux virtual machine in my windows machine, but I don't want my network admin see the Linux VM. Is there any way to hide it?
That depends on how you allow your VM to access the network.
If you allow the VM to access the network through NAT it should be pretty hard to spot as it doesn't get an IP-address. (It sort of hides behind the host's network.)
Note that a competent network admin can probably find it anyway if he went out of his way to find it.
firewall the machine, reject icmp packets so it wont ping, and only allow inbound connections which are related and established to outbound ones. This should be good enough, more or less.
maybe also setup port knocking if you want to get in from outside.