This paper presents a simple surface-potential based drain current (Id) model for gate-allaround carbon nanotube field effect transistor (GAA-CNFET). The model captures a number of features which include ballistic transport, first subband minima, chirality and non-existence of fringing and screening effect due to its geometry. Further, the effect of chirality on subthreshold swing (SS), current on/off ratio (ION/OFF) and transconductance (gm) is studied by extracting these parameters from drain current variation. It is observed that there exists a trade-off between the parameters for different chiral vector CNTs. As chirality increases, transconductance and subthreshold slope increases while current on/off ratio reduces. To confirm the validity of proposed model, virtually fabricated GAACNFET device performance was simulated and compared with the calculated values. The variation is also compared with the experimental result of actually fabricated device. The close match between calculated, simulated and experimental results confirms the validity of the proposed model.