Economic dispatch (ED) aims to minimize the generation cost subject to power balance constraints. It is extensively used in power system operation and planning. ED problem as well as other problems with the same formulation are named as ED-type problems in this letter and a fast solution method is provided. The proposed method is achieved by solving a series of relaxed problems. With a closed-form solution for the relaxed ED-type problems, it is demonstrated that the proposed method consumes far less computing time and memory space than the off-the-shelf solvers and other quadratic programming (QP) methods. Finally, the effectiveness and computational efficiency of the proposed method are verified by the case studies, which shows the great potential in power system planning and operation.