The evolution of interface morphology for a single-phase Nickel-Copper binary alloy in directional solidification is studied by using a phase-field model cooperated solute concentration gradient corrections. The effect of pulling velocity V and strength of the crystalline anisotropy γ on interface morphology and the solute segregation is formulated. The results indicate that, the transition from plane to cells/fine cellular structures, then to planar structures(plane-cell-plane) will happen with the increment of V, and the level of solute trapping becomes stronger. When the crystal grows with cellular structures, γ crucially influences the interface pattern formation at the lower growth velocity, but the solute partition ratio is not significantly affected by the anisotropy strength. Then, the operating behavior for planar growth is hardly any affected by the crystalline anisotropy.