  In this paper, we aim to investigate the mixed Chen-Lee-Liu derivative
nonlinear Schr\"{o}dinger(CLL-NLS) equation via the Riemann-Hilbert(RH) method.
we construct a RH problem base on the Jost solution of the Lax pair. By solving
this RH problem corresponding to the non reflection case, the N-soliton
solution of CLL-NLS equation is obtained, which expression is the ratio of
$(2N+1)\times(2N+1)$ determinant and $2N\times2N$ determinant.
