Broad-area lasers (BA) are practical for producing high output power. However, under a high current operation, high-order modes are easily excited, resulting in the broadened linewidth. Here, based on mode engineering of double-side transverse photonic crystals (TPCs) combined with a longitudinal high-order surface grating, a narrow-linewidth electrically-pumped broad-area laser with high power emission only using I-line lithography is demonstrated. By matching the high-order modes of the wide main waveguide with TPC bands, the effective volume of the high-order modes is expanded, while the fundamental mode remains unchanged. Then, single-lateral mode operation is achieved by selective pumping only for the main waveguide due to the significant distinction in modal gain between the fundamental mode and the high-order modes. In addition, a 27-order grating is constructed above the main waveguide to keep the laser operating in single-longitudinal mode. In the experiment, the device shows an output power of 115 mW, a lasing wavelength of 1552.94 nm with a side-mode suppression ratio (SMSR) of 59.26 dB, a narrow linewidth of 443 kHz, and a relative intensity noise (RIN) < -135 dB/Hz at 600 mA, thus has the potential to meet the needs in fields such as coherent optical communication and LiDAR.