A novel scheme for integrated optical filters with narrow bandwidth is proposed to dramatically improve its compactness on the basis of slow-light waveguide, which provides a large optical path in a short geometry length. By introducing the one-dimensional grating waveguide (ODGW), a kind of slow-light waveguide, into a micro-ring resonator (MRR), the area of MRR is reduced by three orders of magnitude compared to the MRR without ODGW. As a proof of concept, an ultra-compact on-chip filter with narrow bandwidth of 2.1 pm (263 MHz) is conceived by cascading six MRRs with ODGW. Additionally, the designed optical filter shows excellent performances of roll-down speed, out-of-band signal suppression, and in-band ripple. Our proposal offers a promising solution to miniaturize the integrated optical filters with narrow bandwidth, and hence improve the integration density of on-chip photonic networks.