The shape memory properties and microstructure of Fe41Ni28Co17Al11.5(Ti+Nb)2.5 (at.%) cold-rolled alloys were studied at the first time using the values reported in constant stress thermal cycling experiments in a three-point bending test. Thermo-magnetization curves of 97% cold-rolled and solution-treated sample aged at 600 °C for 24, 48 and 72 h showed evidence of the martensitic transformation, and the transformation temperatures increased their values from 24 to 72 h. The alloy cold-rolled to 97% and then solution-treated at 1277 °C for 1 h showed that most grains were aligned near <100> in the rolling direction in the recrystallization texture. The intensity of texture was 13.54, and an average grain size was around 400 μm. The sample aged at 600 °C for 48 h showed fully recoverable strain up to 1.6% at 200 MPa stress level in the three-point bending test. However, the experimental recoverable strain values were lower than the theoretical values, possibly due to the small volume fraction of low angle grain boundary, the formation of brittle grain boundary precipitates, and a grain boundary constraint lower than the expected intensity of texture in the samples.