This paper proposes a crosscorrelation phase shift scheme to improve the performance of linear joint detection. For the calculation of crossorrelation matrix with original outputs of matched filters brings loss due to inter symbol interference(ISI) in linear multiuser detection, the scheme considers ISI as linear combination of multipath delay and spreading code, and proposes a crossorrelation matrix phase shift (CPS) algorithm with channel estimation to equalize the loss analyzed above. A structure integrates CPS with MMSE-PIC to realize the joint detection (JD), and is compared with RAKE-MMSE-PIC multiuser detection in approximately synchronized CDMA systems. Simulations presented for BER and capacity show that the algorithm brings substantial improvement in combating against ISI, but weakens the robustness of JD compared with RAKE-MUD when the multipath fading becomes serious.