We investigated the structural and magnetic properties of Cr1−δTe thin films grown on CdTe(001) layers by molecular beam epitaxy (MBE) with systematic variations of the ratio between Cr and Te fluxes and the substrate temperature Ts during the growth. Cr1−δTe of the hexagonal structure (hex-Cr1−δTe) was always formed irrespective of the growth conditions, but the growth orientation was different depending on the Cr/Te flux ratio and Ts. Hex-Cr1−δTe was grown in the [0001] axis in the range of small Cr/Te ratios and high Ts while it was also grown in the direction normal to the (1–102) plane at larger Cr/Te ratios or lower Ts. Hex-Cr1−δTe films grown in the both orientations show ferromagnetism, but they exhibit a clear contrast in the field dependence of perpendicular magnetization at 2K; a square hysteretic loop in the film grown in the [0001] axis versus a round-shape loop in the film grown in the direction normal to the (1–102) plane. Moreover, the films grown in the [0001] axis at the smallest Cr/Te ratio show variations of ferromagnetic properties with Curie temperature (Tc) and the coercivity (Hc) varying according to the value of Ts.