In order to identify quickly and accurately the load state of structures in some complex environments, a non-iterative inversion method based on finite element method and Newmark method is proposed. By exploring the relationship between measurement data and loads that need to be identified, the error function is established. Based on the least square method and the matrix decomposition scheme, the formulas are derived without iteration process. To improve the inversion accuracy and efficiency in the identification of dynamic loads, the basis function expansion and the singular value decomposition method are adopted. Several different structures are considered to verify the influence of some factors on the inversion results, such as the basis function expansion, the computational time, the measurement noise, the number of measurement points and the location of measurement points. Numerical examples show that the present method can obtain the stable and accurate identifying results.