<p>This paper presents a meshfree Jacobi moving least squares (MJMLS) method for the dynamic analysis of functionally graded conical-cylindrical-annular coupled shells (CCACSs). The CCACS is decomposed into three conical shells, three cylindrical shells, and two annular plates. The modified variational principle and first-order shear deformation theory (FSDT) are used to establish the equations of motion for each shell segment. The equations of the whole system are obtained using the coupling conditions between individual shell segments. A meshfree moving least squares shape function is constructed using a Jacobi polynomial basis with fast convergence and high accuracy. The displacement components of the CCACS are expanded using the meshfree shape function and Fourier series in the meridional and circumferential directions, respectively. Comparisons with numerical results from published literature and the commercial software ABAQUS show that the proposed method is accurate and reliable for predicting the dynamic behavior of CCACS.</p>