This paper presents SSLIDE, Sound Source Localization for Indoors using DEep learning, which applies deep neural networks (DNNs) with encoder-decoder structure to localize sound sources with random positions in a continuous space. The spatial features of sound signals received by each microphone are extracted and represented as likelihood surfaces for the sound source locations in each point. Our DNN consists of an encoder network followed by two decoders. The encoder obtains a compressed representation of the input likelihoods. One decoder resolves the multipath caused by reverberation, and the other decoder estimates the source location. Experiments based on both the simulated and experimental data show that our method can not only outperform multiple signal classification (MUSIC), steered response power with phase transform (SRP-PHAT), sparse Bayesian learning (SBL), and a competing convolutional neural network (CNN) approach in the reverberant environment but also achieve a good generalization performance.