The element-free Galerkin method (EFGM) is improved with partition of unity quadrature (PUQ).Partition of unity quadrature is shown strictly with finite covering and partition of unity.Using Shepard functions as partition of unity functions,we obtain good results.The EFGM with PUQ is a true meshless method. Computational results of EFGM with partition of unity quadrature are more accurate than those of the traditional EFGM with background quadrature.