It is well known that computer has been widely used in almost all fields. In this paper, Hirota's bilinear method with computer symbolic computation is extended to a new AKNS hierarchy with variable coefficients. As a result, one-soliton solutions and two-soliton solutions are obtained. Through the analysis of the obtained one-soliton solutions and two-soliton solutions, a uniform formulae of n-soliton solutions are derived. It is shown from computer running that the obtained one-soliton solutions and two-soliton solutions satisfy the AKNS hierarchy.