This study investigates the grain morphology, microstructure, magnetic properties and shape memory properties of an Fe41.265Ni28.2Co17Al11Ta2.5B0.04 (at%) high-entropy alloy (HEA) cold-rolled to 98%. The EBSD results show that the texture intensities of the samples annealed at 1300 °C for 0.5 or 1 h are 2.45 and 2.82, respectively. This indicates that both samples were formed without any strong texture. The grain morphology results show that the grain size increased from 356.8 to 504.6 μm when the annealing time was increased from 0.5 to 1 h. The large grain size improved the recoverable strain due to a reduction in the grain constraint. As a result, annealing was carried out at 1300 °C/1 h for the remainder of the study. The hardness decreased at 24 h, then increased again at 48 h; this phenomenon was related to the austenite finish temperature. Thermo-magnetic analysis revealed that the austenite finish temperature increased when the samples were aged at 600 °C for between 12 and 24 h. When the aging time was prolonged to 48 h, the austenite finish temperature value decreased. X-ray diffraction (XRD) demonstrated that the peak of the precipitates emerged and intensified when the aging time was increased from 12 to 24 h at 600 °C. From the three-point bending shape memory test, the samples aged at 600 °C for 12 and 24 h had maximum recoverable strains of 2% and 3.6%, respectively. The stress–temperature slopes of the austenite finish temperature were 10.3 MPa/°C for 12 h and 6 MPa/°C for 24 h, respectively. Higher slope values correspond to lower recoverable strains.