Inverse planning is an essential tool for optimizing the delivered radiation dose on low-dose-rate (LDR) prostate brachytherapy. Clinical inverse planning systems use the TG-43 dose computation formalism in order to perform a fast optimization. However, this method is an approximation that often leads to a dose overestimation, resulting on sub-optimal plans. Alternatively, Monte Carlo simulation (MCS) can be used to obtain an accurate dose distribution, but considerably increasing the estimation time. We propose a fast inverse planning method for LDR prostate brachytherapy that uses a deep convolutional neural network (DCNN) trained on a GPU-based MCS generated database to estimate the dose distribution on the prostate and organs at risk. Segmentations of the organs and seeds' positions are given as the DCNN input. The mean percent error on the test set was-1.19±0.94% within the prostate. The DCNN was used to estimate the dosimetric parameters in each organ for every configuration of the optimization loop. The dosimetric parameters of the final DCNN-based brachytherapy plans were in good agreement compared to the same plans recalculated with a full MCS. The proposed inverse planning based on DCNN was capable to reach an equivalent level of accuracy with Monte Carlo with a runtime in less than 1 min using conventional GPU card.