Multiple closed-loop mechanisms are more and more widely used in the mechanical engineering. The precision of the mechanism is one of the key factors in some applications such as the truss structures of space antennas. This paper studies the structural precision of the multi-closed-loop mechanism with joint gaps by combining the improved Jacobian torsor model with the clearance model. Firstly, based on the modified Jacobian torsor model, the errors of the structure caused by joint clearances are calculated. Then the loop relationship of the mechanism with multiple closed loops is analyzed to determine the accuracy of the target points. By using this method, the precision analysis of a deployable truss mechanism in a planer SAR antenna is studied.