Photon sieves, modifications of Fresnel zone plates, are a new class of diffractive image forming devices that open up new possibilities for high resolution imaging and spectroscopy, especially at UV and x-ray regime. In this paper, we develop a novel computational photon sieve imaging modality that enables high-resolution spectral imaging. For the spatially incoherent illumination, we study the problem of recovering the individual spectral images from the superimposed and blurred measurements of the proposed photon sieve system. This inverse problem, which can be viewed as a multi frame deconvolution problem involving multiple objects, is formulated as a maximum posterior estimation problem, and solved using a fixed-point algorithm. The performance of the proposed technique is illustrated for EUV spectral imaging through numerical simulations. The results suggest that higher spatial and spectral resolution can be achieved as compared to conventional spectral imagers.