It is a traditional way to establish parameter estimations and simulations of unbiased grey prediction models by the discrete time response function of whiten differential equation. An novel unbiased grey model based on the high precise direct integration method is proposed without using the discrete time response function. The recurrence relation can be deduced by the exponential matrix of the homogeneous matrix differential equation, written by introducing some new variables, and the unbiased parameters can be derived. Then the simulated values are calculated by using the high precise direct integration method, which can reduce rounding errors and improve precision. It is proved that the proposed method possesses nonhomogeneous law coincidence property and linear transformation consistency. Finally, the validity and utility of the proposed model are verified by rigorous non-homogenous exponential sequence, approximate non-homogenous sequence, monotone sequences and the practical example of car ownership, and the proposed model can improve the precision of simulation and prediction.