The model-based compressive sensing (CS) dictated that robust signal reconstruction was possible to obtain from fewer measurements, but the computational complexity of this approach was large while using the optimal tree approximation with wavelets. Based on the testified result that the wavelet hierarchical tree was still connected, the model-based wavelet hierarchical connected tree CS algorithm， was proposed. The proposed algorithm which has the equivalent measurements with that of model-based CS can enhance the signal-reconstruction efficiency and guarantee the signal-reconstruction accuracy. Numerical simulations demonstrate the validity of the new algorithm. Furthermore, the proposed algorithm has a distinct advantage when dealing with the mass of data.