Smoothed particle hydrodynamics (SPH) is one of the widely used methods to calculate the various astrophysical fluid dynamics. However, standard SPH cannot accurately describe the long-term evolution of shear flows: The large density error emerges within a dynamical timescale, and the amplitude of the error becomes larger than the value of density itself (Δρ ≳ ρ), when we take the mean separation of the particles as the smoothing length. The origin of error is due to the inaccurate description of the continuity equation in the standard SPH formalism. To ensure the local mass conservation property, we have reformulated SPH, in which we distinguish the particle velocity and the fluid velocity for the updation of the particle positions. We find that the present modification provides an accurate description of the density evolution in SPH.