Cemented gangue backfill pier-column (CGBP) which was made of coal gangue, fly ash, cement, and water is the supporting component of the goaf in partial backfill mining or constructional backfill mining for controlling the surface subsidence of coal mining. The width-height ratio and roof-floor strength directly affect the bearing capacity of CGBP under axial compression, which is essential for the design of CGBP. Herein, the effect of width-height ratio (1:3-1:1) on the mechanical characteristics of CGBP with different curing ages under uniaxial compression was system studied through experiment, and the damage process was analyzed by ultrasonic equipment and DIC. Based on the experimental results and discrete element theory, a three-phase numerical model for CGBP was established, which considered the real aggregate shape and distribution and the mechanical characteristics of each phase. Then, the effects of the end friction coefficient and the strength ratio of roof-CGBP-floor combination on the strength and failure characteristics of CGBP (large width-height ratio: 1:1-4:1) were investigated. The results show that CGBP shows the width-height ratio effect obviously and the strength and ductility increase with the increase of the width-height ratio, and the width-height ratio effect increases with the increase of curing age and strength ratio. The end friction constraint is the main reason for the width-height ratio effect, and the higher the friction coefficient is, the larger the width-height ratio effect shows, and the width-height ratio effect disappears without end friction constraint. The increase of the width-height ratio of CGBP and the strength ratio of the roof-CGBP-floor combination increases the strength of the combination. Whether the strength of the combination is greater than that of CGBP may have a roof-floor strength threshold or a strength ratio threshold, which are between 31.44-54.11 MPa and 3.75-6.44, respectively. When the strength of the roof and floor is different, the strength of the combination is mainly controlled by the weak carrier and increases with the increase of the strength of the weak carrier. The peak strain energy of CGBP and combination increases with the increase of end friction coefficient, width-height ratio, and strength of roof and floor. The experimental and simulation results can be used to guide the design of CGBP in constructional backfill mining or partial backfill mining.