Intra-channel nonlinear effects in quasi-linear strongly dispersion-managed transmission are analyzed in detail by numerically solving the multi-pulse coupled modified nonlinear Schrodinger equations. The influences on transmission of intra-channel four-wave mixing (IFWM), intra-channel cross-phase modulation (IXPM), and self-phase modulation (SPM) are compared for different bit patterns, different transmitted powers, and different bit rates. Results show that, in the case of higher bit rate, IFWM is the most important nonlinearity while SPM plays a negligible role as compared to IFWM or IXPM. As the bit rate decreases, both IFWM and IXPM decline while SPM relatively increases. For a fixed bit rate, all of the three nonlinearities increase with the imcrease in input power while IFWM has the fastest increasing rate and SPM the lowest one. We propose to apply a large pre-broadening to the input pulses for quasi-linear strongly dispersion-managed transmission and find that it can efficiently suppress intra-channel nonlinear effects such as IFWM, IXPM and SPM.