The Intelligent reflecting surfaces (IRSs) have been established to show the capability to enhance spectral and energy efficiency by using the passive beamforming at the IRS point and joint optimization of the active beamforming at the base station (BS). However, in the smart wireless environments in which mostly passive RISs are deplored the estimation of the channel state estimation is challenging. This paper, therefore, aims to propose a channel estimation scheme with an improved performance in comparison with some other recently proposed estimation schemes. The proposed channel estimation scheme employs the hybrid strategy to combine the improved versions of traditional Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) compressive sensing algorithms as a basis for the proposed estimator. The proposed estimator, through computer simulations, shows improved performance when compared with the other four channel estimators that were recently documented in literature though with a slightly high computational complexity cost.