The functions of the cost curve and transmission losses are existing nonlinear, simultaneous subject to equality and inequality constraints. Mathematically, the solutions of the nonlinear equations of economic dispatch problems may result in multiple solutions, singal solution or no solution. Conventional methods may fail to find all the multiple solutions if the initial guess values are not appropriately located within the convergency region. To overcome this difficulty the homotopy method is suggested for the solution technique. In this paper the homotopy theorem is incorporated with the B-coefficient method to solve the economic dispatch problem. Not only the initial value is easily obtained but also all the multiple solutions can be obtained. So the exact least cost of economic dispatch can be derived.