Sound source localization (SSL) technology plays a crucial role in various application areas such as fault diagnosis, speech separation, and vibration noise reduction. Although beamforming algorithms are widely used in SSL, their resolution at low frequencies is limited. In recent years, deep learning-based SSL methods have significantly improved their accuracy by employing large microphone arrays and training case specific neural networks, however, this could lead to narrow applicability. To address these issues, this paper proposes a convolutional neural network-based method for high-precision SSL, which is adaptive in the lower frequency range under 1kHz with varying numbers of sound sources and microphone array-to-scanning grid distances. It takes the pressure distribution on a relatively small microphone array as input to the neural network, and employs customized training labels and loss function to train the model. Prediction accuracy, adaptability and robustness of the trained model under certain signal-to-noise ratio (SNR) are evaluated using randomly generated test datasets, and compared with classical beamforming algorithms, CLEAN-SC and DAMAS. Results of both planar and spatial sound source distributions show that the proposed neural network model significantly improves low-frequency localization accuracy, demonstrating its effectiveness and potential in SSL.