This paper combines simultaneous transmitting and reflecting reconfigurable intelligent surfaces （STAR-RIS） with integrated sensing and communication （ISAC） systems to achieve full space communication and awareness. At the same time， a low-cost sensor is applied to STAR-RIS to achieve target sensing on STAR-RIS， solving the serious path loss problem of radar sensing. Based on this， this article researches ISAC system of STAR-RIS assisted multi user multi input single output （MU-MISO） located on both sides of STAR-RIS and a target located on the transmission side of STAR-RIS， aiming to jointly design the active beamforming at the ISAC base station and the passive beamforming matrix of STAR-RIS， in order to maximize communication sum-rate， At the same time， it meets the minimum signal to noise ratio requirements for target perception performance. To solve the non-convex problem in the optimization process， this paper proposes a block coordinate ascending algorithm based on fractional programming， which divides the optimization variables into several block variables for alternate optimization. In the subsequent active and passive beamforming problems of iterative optimization， efficient algorithms such as continuous convex approximation and semi definite relaxation are applied. Simulation results validate the advantages of deploying STAR-RIS in ISAC systems compared to traditional reconfigurable intelligent surfaces. At the same time， the proposed fractional programming-based algorithm is compared with the weighted minimum mean square error algorithm. The simulation results verify the advantages and effectiveness of the proposed algorithm in improving the sum-rate of communication.