It is well-known that the high computational complexity and the insufficient samples in large-scale array signal processing restrict the real-world applications of the conventional full-dimensional adaptive beamforming (sample matrix inversion) algorithms. In this paper, we propose a computationally efficient and fast adaptive beamforming algorithm under small sample support. The proposed method is implemented by formulating the adaptive weight vector as a linear combination of training samples plus a signal steering vector, on the basis of the fact that the adaptive weight vector lies in the signal-plus-interference subspace. Consequently, by using the well-known linear kernel methods with very good small-sample performance, only a low-dimension combination vector needs to be computed instead of the high-dimension adaptive weight vector itself, which remarkably reduces the degree of freedom and the computational complexity. Experimental results validate the good performance and the computational effectiveness of the proposed methods for small samples.