A general and efficient filter-diagonalization method is proposed to solve the quantum mechanical eigenvalue/eigenstate problem in a pre-specified energy range. This method is in similar spirit to the original filter-diagonalization approach, but it eliminates the time propagation by expanding the filter operator directly in the energy space in terms of Chebychev polynomials. Our approach is more efficient than the existing methods because neither time propagation nor time-to-energy transformation is needed. It also allows the choice of the most efficient filter operator for the system of interest. This method is tested for a one-dimensional Morse oscillator and for the two-dimensional Henon-Heiles system. The results show excellent convergence and accuracy.