In this present work, we consider a general subclass $C^*[A,B]$ of close-to-convex functions, which denote by $f(z)=z+\sum\limits_{n=2}^{\infty}a_nz^n$ in $U=\{z:|z|<1\}$ and which satisfy the following condition: $$\bigg|\frac{(zf'(z))'}{g'(z)}-1\bigg|<\bigg|A-B\frac{(zf'(z))'}{g'(z)}\bigg|,\qquad (-1eqslant B