In this paper, we designed efficient conservative numerical schemes for the Zakharov system by leveraging the composition method. The core elements of our approach are as follows. First, the original Zakharov system was transformed into a Hamiltonian system through the use of the variational derivative. Then, the derived system was discretized by integrating the composition method into the Fourier pseudo-spectral method, thus obtaining fully-discrete conservative schemes. These proposed schemes are of the implicit-explicit type and can precisely preserve the discrete mass and Hamiltonian energy. To confirm the theoretical findings and demonstrate the effectiveness and conservation characteristics of our method, we conducted numerous numerical experiments.