In this study, a mode-locked hybrid soliton pulse source (HSPS) utilizing sinusoidal chirped fiber Bragg grating (FBG) is reported for the first time, using the time-domain solution of coupled wave equations and rate equations. The sinusoidal chirped FBG provides a wider bandwidth by adjusting the reversion coefficient or chirp rate even if the FBG length is short. Numerical results also indicate that an HSPS-utilized sinusoidal chirped FBG produces shorter pulses in the $25-72\mathrm{ps}$ range, whereas the pulses range from 31 to $97\mathrm{ps}$ for a linearly chirped tanh apodized grating, and from 30 to $80\mathrm{ps}$ for a linearly chirped Gaussian apodized grating, along with an increase in the mode-locking frequency range.