The elastocaloric effect in Cu-Al-Mn shape memory alloy microwires fabricated by Taylor-Ulitovsky method was investigated. The microwires with bamboo-like grain architecture, homogeneous composition and favorable orientation were successfully prepared through high-temperature annealing heat treatment. The formation of the bamboo grains and high specific surface area contribute to the reduced martensite transformation hysteresis. A large recoverable strain up to 8.8% was achieved by two-way shape memory cycling under a low stress of 50MPa. Consequently, the microwire exhibited a large entropy change S-iso=16.1Jkg(-1)K(-1). Furthermore, the refrigeration capacity (RC) reached similar to 502Jkg(-1) over a working temperature interval T-FWHM=31K during direct transformation under 50MPa uniaxial stress. Finally, a reversible adiabatic temperature change T-ad=3.9K under a stress of 150MPa was obtained. This proves that the present Cu-Al-Mn microwire, with bamboo grains, high refrigeration property and low cost, may act as promising candidate materials for elastocaloric cooling.