The intermodal nonlinear coefficient is an important parameter to analytically describe few-mode fiber (FMF) nonlinearity when the nonlinear interaction arising in the FMF is exploited for various applications. Here, we experimentally characterize the intermodal nonlinear coefficient based on continuous-wave cross-phase modulation, without a priori knowledge of the intramodal nonlinear coefficient for the FMF under test. Based on the derived equation, we examine the impact of the pump modulation scheme and the wavelength spacing between the probe and pump on the precise measurement of the intermodal nonlinear coefficient. Compared with double sideband (DSB) modulation, the pump modulated with carrier-suppressed DSB scheme leads to an underestimation of measurement results, due to the coexistence of unnecessary nonlinear interactions. Finally, the intermodal nonlinear coefficient of a 1.9-km FMF supporting two mode groups is experimentally characterized and is in good agreement with the theoretically calculated values. Due to the random birefringence fluctuation, the average value of 4/3 to describe the intermodal nonlinear interaction arising in weakly coupled FMF by the commonly used Manakov equation is experimentally verified.