The rainbow trapping effect has attracted gathering attention due to its potential application in data processing, energy storage, and light-matter interaction enhancement. The interest has increased recently with the advent of topological photonic crystals (PCs), as the topological PC affords a robust platform for nanophotonic devices. We proposed a chirped one-dimensional (1D) PC as a sandwiched trapped between two1D topological PCs to realize two topological edge states (TESs) for topological protection and trap the formed rainbow. Through graded the thickness of dielectric layers of the chirped 1D PC, light of different wavelengths components localizes and stores at different spatial positions leading to rainbow trapping formation. Unidirectional rainbow trapping can be observed by progressively increasing the thicknesses of the chirped PC. Nonetheless, changing increasingly one of its thicknesses and solidifying the other leads to bidirectional rainbow trapping. Achieving bidirectional rainbow trapping will reduce the footprint of nanophotonic devices in the future. This work brings inspiration to the realization of the rainbow trapping effect and provides a way to design topological nanophotonic devices.