The source directivity is a crucial factor affecting the dipole source identification. At present， the identification methods of dipole sources are usually based on the prior directivity assumption. However， it is difficult to accurately obtain the directivity information of a dipole source in advance. Moreover， the assumption that sources are usually located on a single surface at a certain distance from the microphone array may be not suitable for the actual aeroacoustic system. In order to accurately identify the dipole source under the condition that the directivity of the source is unknown， the equivalent source method based on the reweighted iterative L1 minimization algorithm is proposed in this paper. In this method， the source directivity vector is treated as an unknown quantity and separated from the transfer function relating the measured pressures to the equivalent source strengths， which is solved together with the equivalent source strengths via the weighted iterative L1 minimization algorithm. Then the sound field can be predicted in term of the solved source information. Different from the previous dipole source identification methods， the proposed method can realize three-dimensional volumetric imaging for the dipole sources with unknown directivity. Numerical simulations with three cases of dipole sources with unknown directivities and experiments with the dipole-like sources examine the validity and robustness of the proposed method.