A new numerical method is presented for evaluating the buckling loads of columns with varying cross sections. By this method, the traditional eigenvalue problem is transformed into a special initial value problem, and the buckling loads of the columns can be evaluated by an iteration procedure, which is to satisfy the boundary conditions specified in each case using numerical integrations.. Two numerical examples, a built-up column and a two-component column, are provided for discussion. It is found that the proposed method can meet the precision requirements very well and is a convenient tool for structural designers.