In this work, we design and fabricate a telecom band quantum light source (QLS) on a silicon photonic chip, which integrates a piece of a long silicon waveguide as the nonlinear medium for spontaneous four-wave mixing (SFWM) and five narrow FSR-free bandpass filters based on a grating-assisted contra-directional coupler (GACDC). Two optical filtering functions of the silicon integrated QLS have been demonstrated. First, the QLS supports two tunable outputs of photon pair generations by four GACDC filters. A wavelength tunable range of 6 nm is demonstrated. Second, one GACDC bandpass filter is designed as an on-chip pump filter before the silicon waveguide. The performances of the QLSs with and without the on-chip pump filter are measured and compared. It shows that the on-chip pump filter has the effect to enhance the performance of the QLS by suppressing the Raman noise photons generated when a pump light propagated in optical fibers before it is injected into the chip. These results show that FSR-free filters would play important roles in developing silicon integrated QLSs.