Energy-efficient simultaneous localization and mapping (SLAM) is crucial for mobile robots exploring unknown environments. The mammalian brain solves SLAM via a network of specialized neurons, exhibiting asynchronous computations and event-based communications, with very low energy consumption. We propose a brain-inspired spiking neural network (SNN) architecture that solves the unidimensional SLAM by introducing spike-based reference frame transformation, visual likelihood computation, and Bayesian inference. We integrated our neuromorphic algorithm to Intel’s Loihi neuromorphic processor, a non-Von Neumann hardware that mimics the brain’s computing paradigms. We performed comparative analyses for accuracy and energy-efficiency between our neuromorphic approach and the GMapping algorithm, which is widely used in small environments. Our Loihi-based SNN architecture consumes 100 times less energy than GMapping run on a CPU while having comparable accuracy in head direction localization and map-generation. These results pave the way for scaling our approach towards active-SLAM alternative solutions for Loihi-controlled autonomous robots.