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We calculate the energy of ground state S0 and the first two excited states S1 and T1 of the hydrogen molecule. The corresponding wave function is expanded with the bonding and non-bonding molecular orbitals where each hydrogen atom is represented with one unoptimized Slater type basis function, then all integrations for the energy components evaluations are performed and estimated with the Monte-Carlo method. Unlike the standard method of the Hartree-Fock, the construction of the Fock matrix followed with its diagonalization is circumvented. For considerably large data samplings of 50, 000, the computational time is still cheap, costing just a split of second. At the STO-3G level of theory, the ground state energies show similar accuracy with the Hartree-Fock calculations while superior accuracy for the singlets and triplets reveal with ease the electron correlation effect. [ABSTRACT FROM AUTHOR]