Solving electronic structure problems for large molecules is an important research topic in quantum computational chemistry. Quantum computers provide a possibility for solving these quantum chemistry problems that are intractable classically. In this thesis, we use the hybrid-quantum classical algorithm — variational quantum eigensolver (VQE) to simulate the molecular energies of some simple molecules based on two different kinds of ansatzes and discuss their results. In particular, we illustrate the number of parameters of unitary coupled-cluster with single- and double-excitation (UCCSD) ansatz can be educed without the loss of accuracy in energy difference.