In general, the amplitude-weighting method for an acoustic transducer array is widely used to improve the array directivity and reject disturbances. This paper presents a method to effectively reduce the side lobe level while minimizing the main lobe width increase. This is done using the simulated annealing algorithm (SAA) for a uniformly spaced arc array of omnidirectional underwater acoustic transducers, even at low signal-to-noise ratio (SNR). We propose a new cost function for the SAA and obtain the weighting coefficients for all array elements using the SAA, and next compare them with various amplitude weighting methods. Through simulation and comparison, it is verified that the proposed method is effective in beamforming of the uniform arc array of underwater acoustic transducers.