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Energy consumption of memory accesses dominates the compute energy in energy-constrained robots, which require a compact 3-D map of the environment to achieve autonomy. Recent mapping frameworks only focused on reducing the map size while incurring significant memory usage during map construction due to the multipass processing of each depth image. In this work, we present a memory-efficient continuous occupancy map, named GMMap, that accurately models the 3-D environment using a Gaussian mixture model (GMM). Memory efficient GMMap construction is enabled by the single-pass compression of depth images into local GMMs, which are directly fused together into a globally-consistent map. By extending Gaussian Mixture Regression (GMR) to model unexplored regions, occupancy probability is directly computed from Gaussians. Using a low power ARM Cortex A57 CPU, GMMap can be constructed in real time at up to 60 images/s. Compared with prior works, GMMap maintains high accuracy while reducing the map size by at least 56%, memory overhead by at least 88%, dynamic random-access memory (DRAM) access by at least 78%, and energy consumption by at least 69%. Thus, GMMap enables real-time 3-D mapping on energy-constrained robots.