In this article we have proposed an efficient Ant Colony Optimization method, namely Guided Ant Colony Optimization (GACO) technique for optimizing mathematical functions. The search process of the optimization approach is directed towards a region or a hypercube in a multidimensional space where the amount of pheromone deposited is maximum after a predefined number of iterations. The entire search area is initially divided into 2n number of hypercubic quadrants where n is the dimension of the search space. Then the pheromone level of each quadrant is measured. Now, the search jumps to the region (new search area) of maximum pheromone level and restarts the search process in the new region. However, the search area of the new region is reduced compared to the previous search area. Thus, the search advances and jumps to a new search space (with a reduced search area) in several stages until the algorithm is terminated. The GACO technique has been tested on a set of mathematical functions with number of dimensions upto 100 and compared with several relevant optimizing approaches to evaluate the performance of the algorithm. It is observed that the proposed technique performs better or similar to the performance of other optimization methods.