The propagation of optical pulses in lossless single-mode fibers can be described by the nonlinear Schrdinger (NLS) equation. When the birefringence effect exists and two or more wave packets with different carrier frequencies appear in the system at the same time, the interaction between them is described by the coupled nonlinear Schrdinger (CNLS) equation. CNLS equation is one of the basic models to describe nonlinear phenomena. In nonlinear optics, in order to realize the wavelength division multiplexing, multiple light field must transmit at the same time. Therefore, CNLS is often used to describe the nonlinear phenomenon of optical soliton in WDM system, birefringence fiber, multimode optical fiber, optical fiber array and Bose-Einstein condensates. In particular, the simultaneous transmission of two ultrashort pulses in the fiber can be described by the CNLS equation with higher order terms. Based on the generalized coupled nonlinear Schrdinger equation, and its N-soliton solution, the effects of self-steepening effect and self-frequency shift effect on the propagation characteristics of N-soliton solution are numerically investigated by using the split-step Fourier method. The results show that both the self-steepening effect and the self-frequency shift effect cause the 1-soliton solution to shift during transmission. For the bound soliton form of 2-soliton solution and 3-soliton solution, self-steepening effect and self-frequency shift effect causesoliton shift and energy redistribution. For 2-soliton solution and 3-soliton solution with breathing-like structure, self-steepness effect and self-frequency shift effect destroy the breathing structure, making the solution split into several solitons with different amplitudes and transmission speeds.