In this paper, we study a multiple-input single-output (MISO) assisted multi-user downlink network. To support low-latency communications, the transmissions to massive users are coded by finite blocklength (FBL) codes. For such network, an efficient power allocation design is provided to optimize the sum throughput. In particular, we first characterize the FBL throughput performance, following which a power allocation problem is formulated aiming at maximizing the sum throughput in the FBL regime. To address the formulated non-convex problem, we separate the complex expression of the objective function into two parts and then conduct different tight convex approximation methods, with which, an efficient successive convex approximation (SCA)-based approach is introduced. Simulation results validate our analytical model and reveal that the proposed approach converges effectively and achieve the performance close to results of the exhaustive search. Furthermore, we evaluate the impacts of blocklength, number of transmitter antennas, power constraints and number of users on the system performance.