In this paper, we propose a novel test methodology for core-based system LSIs. Our test methodology aims to decrease testing time for core-based system LSIs. Considering testing time reduction, our test methodology is based on BIST and ATPG. The main contributions of this paper are summarized as follows. (i). BIST is efficiently combined with external testing to relax the limitation of the external primary inputs and outputs. (ii). External testing for one of cores and BISTs for the others are performed in parallel to reduce the total testing time. (iii). The testing time minimization problem for core-based system LSIs is formulated as a combinatorial optimization problem to select the optimal set of test vectors from given sets of test vectors for each core.