To use a small number of acoustic pressure measurement data to reconstruct the radiated acoustic field of the complicated structure, a theory of source strength density acoustic radiation modes is proposed and a formula of acoustic field reconstruction is developed. In the space defined on the surface of the structure, functional form of the acoustic radiation power expression in which parameter is source strength density is constructed. In terms of the functional a linear self-adjoint and positive radiation operator is defined whose eigenfunctions are source strength density acoustic radiation modes. And then it is proved that source strength density acoustic radiation modes possess space filter characteristic through analyzing the source strength density radiation modes of rectangular plate and cylinder with hemisphere ends. The formula of acoustic field reconstruction with the space filter nature is obtained. The sphere simulations and plate experiment validate the feasibility and robustness of the proposed acoustic field reconstruction method. The acoustic field reconstruction method based on the proposed radiation modes is simple, has high accuracy that can be obtained by using only a few measurement data, so this method is especially applicable for low frequency acoustic field reconstruction of the complicated structure.