A multireference Moller-Plesset (MRMP) method with a complete active space configuration interaction (CASCI) reference function has been proposed as an accurate and computationally efficient method for treating the ground and excited states of molecules. The CASCI wave function was constructed using the self-consistent field orbitals and used as a reference function of the MRMP to incorporate the remaining dynamical correlation. The advantage in using the CASCI is that it does not require iterations, nor does it encounter convergence difficulties which may be found in complete active space self-consistent field (CASSCF) calculations. The scheme was applied to the potential curves of the ground and low-lying excited states of N-2, the potential curve of the ground state of CO, and the vertical valence pi-pi* excited states of benzene. Excellent agreement between theory, experiment, and some benchmark calculations was obtained. MRMP with CASCI is comparable in accuracy with MRMP with CASSCF. The present scheme will open a possibility toward accurate treatment for the ground and excited states of small to large molecular systems.