Using nano-enhanced phase change materials is a widespread passive method to improve the melting performance, and also the storage capacity of the thermal energy storage units. In this study, the effects of CuO nanoparticles (0≤φ≤1.5%) and new proposed stair fins on the efficiency improvement of latent heat thermal energy storage units are investigated. The stair fins are arranged in both upward and downward directions from the heated walls and the stair ratio is in the range of 0.67≤b/c≤4.0. One of the vertical walls of the PCM enclosure is subject to uniform temperature and the other three walls are insulted. The numerical results show that by adding nanoparticles with volume concentration of φ=1.5% for b/c = 0.67 to the flow, the energy storage capacity is enhanced by 9.1% compared to the pure PCM with downward fins. The maximum energy storage capacity of 474.1 kJ is achieved by using descending stair fins with b/c = 4.0 and φ=1.5% which is much higher compared to the cases without nano additives. Besides, the melting performance is significantly improved by adding the nanoparticles. In fact, nanoparticles improve the thermal conductivity of the fluid and also act as a heat sink to absorb the heat from the fins. The downward fins with larger stair ratios (b/c = 4.0) perform significantly better than the upwards ones which is because of the free convection effects and the recirculations flows on the upper face of these fins.