Firstly, from the perspective of subspace alignment, the joint optimization problem of the interference signal power and the useful signal power is modeled on the Grassmannian manifold. The constrained optimization problem is transformed into the unconstrained optimization problem with lower dimension. Then, using the geometric properties of the Grassmannian manifold, a joint interference alignment precoding scheme based on conjugate gradient algorithm on the Grassmannian manifold is proposed. Computer simulation results show that the proposed scheme improves the sum rate performance of the multiuser MIMO interference system by jointly considering the minimization of the interference signal power and the maximization of the useful signal power, and also improves the convergence speed by effectively solving the 90° turning problem of the Grassmannian steepest descent algorithm.