Let u, v be the analytic functions on the open unit disk D in the complex plane, \varphi the analytic self-map of D and m a nonnegative integer, n a positive integer that is greater than m. We consider the generalized Stevi\’{c}-Sharma type operator T_{u,v,\varphi}^{m,n}f(z)=u(z)f^{(m)}(\varphi(z))+v(z)f^{(n)}(\varphi(z)) acting from the derivative Hardy spaces into Zygmund-type spaces, and investigate its boundedness, essential norm and compactness in this paper.