In this paper, a novel algorithm called logic depth oriented (LDO) common subexpression elimination (CSE) is proposed. In order to avoid the increase of logic depth in circuit structure that may be caused by the application of some other CSE techniques, the process of common subexpressions eliminating of this algorithm is logic depth oriented and the realization of logic operators reuse will not lead to the increase of logic depth. A complete description of the LDO algorithm and the comparisons with several popular CSE algorithms are presented in this paper. Results of comparisons show that using this algorithm can realize the logic operators reuse efficiently, while the logic depth in circuit structure will maintain optimal. Application of this method in the multiplierless VLSI implementation of high-speed FIR filters or some other multiple constant multiplication (MCM) problems will contribute to the high performances in several aspects such as area, speed and power dissipation.