Traditional Voice activity detection (VAD) algorithms are applied in a linear transformed space without any constraint. As a result, the VAD algorithms are not robust to noise interference. Considering the special characteristics of speech, we proposed a new speech feature extraction method by giving constraints on the processing space as a reproducing kernel Hilbert space (RKHS). In the RKHS, we regarded the speech estimation as a functional approximation problem. Under this framework, we could incorporate the nonlinear mapping functions in the approximation implicitly via a kernel function. The approximation function could capture the nonlinear and high-order statistical regularities of the speech. Our VAD algorithm is designed on the basis of the power energy in this regularized RKHS. Compared with a baseline and G.729B VAD algorithms, experimental results showed the promising advantages of our proposed algorithm.