The problem of direction of arrival (DOA) estimation of non-circular (NC) signal for non-uniform linear array is investigated. A generalised-ESPRIT (GESPRIT) algorithm can be treated as an improvement of ESPRIT algorithm and the inter-elements spacing of the array geometry can be uniform or non-uniform within a half wavelength. The authors combine the GESPRIT algorithm and the NC property, and propose an NC-GESPRIT algorithm to obtain the DOAs of NC signals, which requires spectrum peak searching. Moreover, a computationally efficient search-free root NC-GESPRIT algorithm, which is based on polynomial rooting, is also proposed to depress the computational cost. The proposed NC-GESPRIT algorithms have much better estimation performance than the conventional GESPRIT algorithm and it can detect 2M-1 sources with only M sensors due to the NC property. Furthermore, the proposed algorithms can work well without estimating NC phase. The effectiveness and improvement of the proposed algorithms will be proved in the following simulation results.