While calculating the bound state energy eigenvalues of a superlattice, the wave functions on both sides of the interface between a potential well and a potential barrier are extended into a set of linear equations which can be described with a matrix equation. Then, according to the requirement that the energy eigenvalues must satisfy the condition in which the coefficient determinant of linear equations is equal to zero, the energy region is scanned point by point. Thus, the corresponding energy eigenvalues can be determined with a function of the matrix determinant in MATLAB. Compared with other methods such as iteration and transfer matrix, the method does not need more efforts in programming and is simple in concept, convenient in operation and practical.