By considering the separable convex optimization problems with linear constraints, their objective function can be divided into three independent convex functions without coupling variables. Based on the extension of alternating direction of multipliers, this paper presents a new partial predictioncorrection splitting method for solving separable convex optimization problems, this algorithm considers that the first variable is not corrected in correction step but the second variable and third variable are corrected. In addition, the convergence of this algorithm is proved under weaker condition.