It is well-known that most wavelet functions are unsymmetrical and thus fail to satisfy Fourier criterion. These kinds of wavelets cannot be utilized to construct Mercer kernel directly. Based on convolution technique, this paper proposes a novel framework on Mercer kernel construction. The proposed methodology indicates that any of wavelets can generate a wavelet-like kernel basis function, which has zero vanishing moment. An example on convolution Mercer kernel construction is given by using Haar wavelet. The self-constructed Haar wavelet convolution kernel (HWCK) function is then applied to kernel subspace linear discriminant analysis (SLDA) approach for face classification. The eMU PIE human face dataset is selected for evaluation. Comparing with the RBF kernel based SLDA method and existing LDA-based kernel methods such as KDDA and GDA, the proposed Haar wavelet convolution kernel based method gives superior results.