Full waveform inversion is a technique for determining the optimal model parameters by minimizing the data misfit. Depending on the frequency content of the data, the objective function may be highly non-linear. This problem particularly prevents the methods from recovering the low frequency components of the velocity model. In this paper, we propose a modified version to solve this problem by breaking the gradient formula into four terms after wave field decomposition and then by using proper terms to invert the high frequency and the low frequency components alternately. Numerical tests of a simple 2D synthetic model show that this new method is efficient at recovering the low frequency components of the velocity model, at least on this particular example.