The Multiple Constant Multiplications (MCM), i.e., the multiplication of a variable by a set of constants, has been a central operation and performance bottleneck in many digital signal processing applications such as, image and video processing. digital television. and wireless communications. Since the design of multiplications is expensive in terms of area, delay, and power consumption in hardware., the area-delay optimization of the MCM operation has often been accomplished by using the shift-adds architecture. However, most of the previously proposed algorithms have focused on the optimization of area ignoring the crucial tradeoff between area and delay of the computation. In this paper, we introduce an approximate algorithm that can find near optimal area Solutions under the user specified delay constraint. It is shown by the experimental results that the proposed algorithm finds better area-delay solutions than the previously proposed efficient algorithms.