Abstract: ‍ ‍Applications such as radar， sonar， and wireless communications have heightened demands for improved anti-jamming capabilities and real-time performance in adaptive beamforming. Traditional adaptive beamforming algorithms that rely on the steepest descent method often exhibit an “overfitting” characteristic， which hinders their ability to effectively suppress interference. Furthermore， these algorithms struggle to manage interference when it involves perturbations and mismatches in the steering vector. To tackle these challenges， this paper proposes a quadratic constraint-wide nulling interference suppression method for adaptive beamforming， accelerated by the conjugate gradient （CG） algorithm. The proposed method first utilizes the rapid convergence properties of the CG algorithm to solve the linear equations relating the sample covariance matrix to the steering vector. The weight vector generated by the CG algorithm serves as the initial weight for the steepest descent beamforming method， leveraging the “overfitting” characteristic to ensure robust locking onto the desired signal. Additionally， we propose a direction of arrival （DOA） estimation method to enhance interference feature extraction， enabling the estimation of interference arrival directions in the presence of wideband coherent interference. This method works in conjunction with the quadratic constraint null broadening technique to capture and adaptively nullify interference characteristics. Simulation experiments confirm that the proposed algorithm efficiently adapts to suppress interference under both single snapshot and wideband coherent interference conditions while demonstrating strong robustness.