A novel multiuser communication system with movable antennas (MAs) is proposed, where the antenna position optimization is exploited to enhance the downlink sum-rate. The joint optimization of the transmit beamforming vector and transmit MA positions is studied for a multiuser multiple-input single-input system. An efficient algorithm is proposed to tackle the formulated non-convex problem via capitalizing on fractional programming, alternating optimization, and gradient descent methods. To strike a better performance-complexity trade-off, a zero-forcing beamforming-based design is also proposed as an alternative. Numerical investigations are presented to verify the efficiency of the proposed algorithms and their superior performance compared with the benchmark relying on conventional fixed-position antennas (FPAs).