Retrieval of magnetization parameters using magnetic tensor gradient measurements receives attention in recent years. Determination of subsurface properties from the observed potential field measurements is referred to as inversion. Little regularizing inversion results using full tensor magnetic gradient modeling so far has been reported in the literature. Traditional magnetic inversion is based on the total magnetic intensity (TMI) data and solving the corresponding mathematical physical model. In recent years, with the development of the advanced technology, acquisition of the full tensor gradient magnetic data becomes available. In this paper, we study invert the magnetic parameters using the full tensor magnetic gradient data. A sparse Tikhonov regularization model is established. In solving the minimization model, the conjugate gradient method is addressed. Numerical and field data experiments are performed to show feasibility of our algorithm.