Light-field near-eye displays can solve the accommodation/convergence conflict problem that can cause severe discomfort to the user. However, in actual systems, convergence depth and accommodation depth may not match each other due to the repeated zones or flipped images produced by traditional light-field methods. Also, Moiré fringes are another problem which is caused by interaction between two periodic structures. We present a method of constructing a light-field near-eye display based on random pinholes, where the random structure is employed as a spatial light modulator to break the periodicity of elemental images. Light-field images for a unique view zone in space without Moiré fringes can be provided. A proof-of-concept prototype has been developed to verify the proposed method.