Calcium imaging has been widely used for measuring spiking activities of neurons. When using calcium imaging, we need to extract summarized information from the raw movie beforehand. Recent studies have used matrix deconvolution for this preprocessing. However, such an approach can neither directly estimate the generative mechanism of spike trains nor use stimulus information that has a strong influence on neural activities. Here, we propose a new deconvolution method for calcium imaging using marked point processes. We consider that the observed movie is generated from a probabilistic model with marked point processes as hidden variables, and we calculate the posterior of these variables using a variational inference approach. Our method can simultaneously estimate various kinds of information, such as cell shape, spike occurrence time, and tuning curve. We apply our method to simulated and experimental data to verify its performance.