Surface-enhanced Raman spectroscopy (SERS) is widely used to sensitively detect molecules or markers in pharmacology, biology, etc. We study numerically the possibility to realize SERS detections directly on a photonic chip. It is presented that a SERS sensor created by combining a gold slot waveguide and a Si3N4 strip waveguide can be designed to excite enhanced Raman effects and extract their scattering signals on a chip. Using 3D finite-difference time-domain simulations, the SERS processes, excitation of surface plasmon in slots and radiation of induced Raman dipoles, are analyzed to simulate SERS detections in reality. It demonstrates the influence of the geometrical parameters on the electromagnetic fields in slots and therefore the local enhancements, based on the |E|4-approximation. The results show that a SERS nanosensor can be achieved based on the hybrid waveguide. The integration of this sensor with a micro-laser and a micro-demultiplexer, could achieve an on-a-chip and fully integrated system for portable and fast SERS detections.