We propose a novel adaptive image interpolation method based on the weight classified vector quantization (CVQ) using optimal coefficients which are constrained by a quadratic signal class. It overcomes the computational complexity bottleneck of other second-order image interpolation methods such as an edge-directed and an optimal recovery interpolation. Our proposed interpolation method consists of three steps: the coefficient generation step constructing both image patches and constrained coefficient sequences from a set of training images, weight CVQ step generating codevectors from classified image patches, and interpolation step using an equal-average nearest neighbor search (ENNS). Simulation results with exemplary test images demonstrate that our proposed method is superior to a bilinear and a bicubic interpolation. Moreover, its visual quality is comparable to that of the edge-directed and the optimal recovery interpolation, with the much less computational load.