Long integration is often required to detect weak moving target in sea clutter. However, the Doppler frequency spread and amplitude fluctuation in long integration and limited reference cells resulting from spatial non-homogeneity of sea clutter make the traditional adaptive detector work badly. By observing that the Compound Gaussian Distribution (CGD) with Inverse Gamma (IG) texture gives a good fit to sea clutter and the instantaneous frequency is slowly varying, a combined adaptive detector, namely the Combined Adaptive Generalized Likelihood Ratio Test-Linear Threshold Detector (CA-GLRT-LTD), is proposed in the paper, which consists of the product of the maximal response of the adaptive GLRT-LTD in several continuous short integration intervals. Owing to the optimality of the GLRT-LTD for CG clutter with IG texture, the proposed detector obtains better performance than the Combined Adaptive Normalized Matched Filter (CANMF) detector.