I read about CNT doping in CNTFET that beneath the gate CNT should be intrinsic and source and drain are n/p doped. But if I compare it with MOSFET, shouldn't the CNT beneath gate be doped with opposite doping as source/drain region and channel would be created by inversion?
You should consider why the body is doped in a MOSFET. Then you would see that there is no strong reason to dope the CNT in a CNTFET.
The main reason one uses doping in the body of a MOSFET is to have short depletion regions between the body and the contacts, so that you have good electrostatic control of the channel and you can scale the device down. In a CNT you typically have good electrostatic control because the body is very thin, therefore this reason disappears. Indeed, also in ultra-thin-body MOSFETs, CMOS technology uses undoped of very lightly doped bodies.
There are several other second-order reasons to use doping in the body of a MOSFETs, but are much less important.
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