Compressive sensing (CS) with sparse random matrix for the random sensing basis reduces source coding complexity of sensing devices. We propose a downsampling scheme to this framework in order to further reduce the complexity and improve coding efficiency simultaneously. As a result, our scheme can deliver significant gains to a wide variety of resource-constrained sensors. Experimental results show that the computational complexity decreases by 99.95% compared to other CS framework with dense random measurements. Furthermore, bit-rate can be saved up to 46.29%, by which less bandwidth is consumed.