In this paper, we propose a partially parallel prediction-correction splitting method for solving block-separable linearly constrained convex optimization problems with three blocks. Unlike the extended alternating direction method of multipliers, the last two subproblems in the prediction step are solved parallelly, and a correction step is employed in the method to correct the dual variable and two blocks of the primal variables. The step size adapted in the correction step allows for major contribution from the latest solution point to the iteration point. Some numerical results are reported to show the effectiveness of the presented method.