Using the FLAC3D multi-fracture constitutive relation, a numerical model of anisotropic failure characteristics of a layered rock slope was established. With the strength reduction method, the relationships between the slope safety coefficient and the interlayer weak plane dip angle β, slope angle α, slope height H, and shear strength of the rock mass were determined, and the impacts of various factors on the safety coefficient were investigated with the grey correlation method. Results show that for a bedding slope(with the slope direction consistent with the obliquity of the rock layer)at β ≤15°, damage is mainly caused by tensile cracking-shear-slippage failure, and a sliding surface does not occur along the interlayer weak plane; bedding slippage failure appears at 15°<β<α; and the top of the slope slips along the weak plane, and bending failure appears at the slope foot at β≥α. For a reverse slope(with the slope direction opposite to the obliquity of the rock layer), the compression-shear failure is the main failure mode at β<50°, and toppling failure appears when β is larger(β≥50°). With the increase of β, the safety coefficient of the bedding slope shows a tendency to decrease first, then increase, and then decrease again, and the stability of the horizontal layered slope is higher than that of the vertical one. The safety factor change tendency of the reverse slope is opposite to that of the bedding slope. In the case of β>α, the stability of the bedding slope is higher than that of the reverse slope at the same dip angle. For a bedding slope, the slope height has the greatest impact on the stability, followed by the cohesion of the weak plane and slope angle, and the influences of the dip angle and friction angle of the weak plane are relatively small; for a reverse slope, the influence of each factor on its stability is ranked by the friction angle of the weak plane, slope angle, slope height, and cohesion and dip angle of the weak plane.