The 2 × 2 3-dB couplers are one of the most widely used and important components in silicon photonics. Here, we propose an ultra-broadband and compact 2 × 2 3-dB adiabatic coupler defined by b-splines and optimized with an efficient supermode-injected adjoint shape optimization. By employing mode adiabatic evolution and mode coupling at two different wavelength ranges, respectively, we achieve an ultra-broad bandwidth of 530 nm from 1150 nm to1680 nm with a power imbalance below ±0.76 dB in a compact coupling length of 30 µm according to our simulation results. The supermode-injected adjoint shape optimization can also be applied to the design of other photonic devices based on supermode manipulation.