Neuromorphic computation has been a hot research area over the past few years. Memristor, as one of the neuromorphic computation materials retains the conductance value and is able to adapt it with the changing input voltages. This paper pioneers in a neuromorphic computing paradigm implementation (through memristor) for Extreme Learning Machine (ELM), which has been one of most popular machine learning algorithms. By simulating the biological synapses with memristors and combining the memory property of memristor with high-efficient processing ability in ELM, a three-layer ELM model for regression is constructed and implemented. The ELM network weights are represented through the memristive conductance values. The conductance values (network weights) are updated through tuning the voltages. Experimental results over the canonical machine learning dataset show that the memristor-based ELM achieves the same level of performance as the one implemented via traditional software, and exhibits great potential that ELM can be implemented in neromorphic computation paradigms.