Nuclear magnetic resonance gyroscopes (NMRGs) have broad application perspectives with the advantages of low cost, low power consumption, miniaturization-ability and high precision. The transverse relaxation rate of noble gas nuclear spins is used to evaluate the performance of vapor cell, which also affects the angle random walk (ARW) of NMRG systems. The inhomogeneity of electronic spin polarization spatial distribution is one of the essential sources of the transverse relaxation rate. In this paper, we study the influence of the pump power and beam diameter in the transverse relaxation rate of noble gas nuclear spins through numerical simulations of electronic spin polarization and experimental measurements of transverse relaxation time. Simulations of the electronic spin polarization spatial distribution are proposed based on the Bloch-Torrey equations. The transverse relaxation time of noble gas nuclear spins under different pump power and beam diameters is measured by the free induction decay (FID) method. Experimental results show that the transverse relaxation rate of nuclear spins increases with pump power. The relaxation rate with a 2.3mm pump beam diameter is larger than with a 1.3mm diameter. Furthermore, we innovatively find that the transverse relaxation rate shows a linear relationship with the electronic spin polarization obtained from the numerical simulation. This work provides a reference for the study of nuclear spin relaxation and the optimization of the parameters of the pump beam in NMRGs.