Considering that the interference suppression capability of the existing adaptive beamformer decreases when coupling the array element position error, amplitude and phase error, and signal arrival direction error, a robust adaptive beamforming algorithm based on eigenspace bases transition was proposed. First, the influence of the array element position error, amplitude and phase error, and signal arrival direction error of the steering vectors was modeled. Then, on the basis of the characteristics that the real signal subspace was the same as the space spanned by the steering vectors, the concept of subspace distance was introduced to quantify the similarity of two subspaces, and a multi-dimensional nonlinear optimization problem that minimized the spatial distance was constructed. Next, a hybrid optimization strategy was formed by combining the characteristics of the genetic algorithm and the quasi-Newton method, and after solving the optimization problem, a set of non-orthogonal bases of the signal subspace were obtained. Finally, the estimated signal subspace and the noise subspace were combined into an eigenspace. The accurate interference-plus-noise covariance matrix was extracted by the bases transition of the eigenspace, and the steering vector of the desired signal was corrected. Numerical simulation results show that the proposed hybrid optimization algorithm could significantly reduce the subspace distance as the number of iterations increased. When the number of iterations reached 100, the subspace distance reduced to less than 1. When the array element position error, amplitude and phase error, and signal arrival direction error occurred at the same time, and the input signal-to-noise ratio was 10 dB, the output signal-to-interference noise of the proposed algorithm was about 14 dB higher than that of the existing methods.