By analyzing the position relation between the seams in inclined and steeply inclined multilayer deposits, this paper deduced a formula to calculate the safe mining height H of multilayer deposits by function fitting method based on the statistical data from some domestic and overseas mines using backfilling method. With a copper mine as an example, an orthogonal experiment considering five factors and five levels was designed for the sensitivity analysis of factors influencing the safe mining height H, and the relationships between the main factors and H were also studied. The results show that seam spacing, orebody dip angle and groundwater have significant impact on the safe mining height H, while geological structure characteristics and Protodyakonov coefficient have less effect. The safe mining height H has a linear positive correlation with the seam spacing, a non-linear positive correlation with the orebody dip angle and a non-linear negative correlation with the effect of groundwater. According to the proposed formula and the parameters of the orebodies and rocks, safe mining height of the copper mine ranges from 3.71 m to 5.38 m. Some suggestions about the mining schemes are also provided.