In this paper, by using new linearization method we present an optimization algorithm for globally solving a class of multiplicative problems which have a broad application in computational chemistry, information technology, and so on. By utilizing characteristic of quadratic function, a series of linear relaxation programming problem of the initial problem can be derived and which can provide a reliable lower bound. By means of the subsequent solutions of a sequence of linear relaxation programming problems, the proposed optimization algorithm converges to the global optimal solution of the initial problem. Numerical experimental results show that the proposed algorithm is feasible and effective.