We observed that the annealing of Co-rich microwire at variable temperature allows to develop graded magnetic anisotropy. In such microwires, annealed with a temperature gradient, gradual variation of the hysteresis loops along the microwire length is observed. While inclined hysteresis loops are observed in as-prepared Co-rich microwires, perfectly rectangular hysteresis loops are obtained for microwires annealed at high enough temperature. Accordingly, single-domain wall propagation is observed in Co-rich microwires segments with rectangular hysteresis loops. In microwire segments annealed at intermediate temperatures, irregular hysteresis loops are observed. The origin of such hysteresis loops discussed considering magnetization rotation and DW propagation contributions. We observed that in Co-rich microwire with graded magnetic anisotropy the domain wall velocity is not uniform.