This paper studies an energy beamforming and time duration joint optimization problem for maximizing the sum-rate of a battery-free-multi-antenna-relay-assisted wireless powered communication network (WPCN). The considered problem is non-convex due to the strongly coupled optimization variables. By introducing new optimization variables and reformulating the problem into a convex problem, the optimal solution is obtained based on convex optimization methods. Furthermore, an alternate iteration algorithm is proposed by decoupling the problem into two subproblems, and a semi-closed form solution of the optimal energy beamforming matrix is derived with given time allocation. Simulation results indicate that the proposed battery-free multi- antenna relay architecture can deliver a significant sum-rate gain for the WPCN. In addition, the proposed suboptimal algorithm only has 5% sum-rate loss compared to the optimal solution.