Porous Cu‐Al‐Ni shape memory alloys (SMAs) were fabricated via powder metallurgy method by using Cu, Al, Ni powders and Cu‐Al‐Ni alloy powder as raw materials, respectively. It is found that the two kinds of specimens have similar macroscopic morphologies: connected pores are uniformly distributed in the Cu‐Al‐Ni matrix, forming a three‐dimensional network structure. By comparison, the specimen fabricated by using alloy powder has much finer microstructures than the specimens fabricated by using Cu, Al, Ni powders. After adding Ce element to the latter, the microstructure of the Cu‐Al‐Ni matrix was significantly refined because of the formation of Ce‐rich particles. Damping tests show that the latter has superior damping capacity than the former. With the increase of Ce content, the damping of the latter increases first and then decreases. When the Ce content reaches 0.05 wt.%, the highest damping can be achieved. Correlated mechanisms were discussed based on the microstructural observations.This article is protected by copyright. All rights reserved.