A fracture mechanics based approach for offshore mooring fatigue assessment was developed. Then both S-N curves and fracture mechanics based fatigue analysis for the mooring system of a floating offshore structure were carried out. The low frequency and the wave frequency load processes were regarded as two random load processes for calculating the tensions along mooring lines excited by motions of low frequency and wave frequency. The dual narrow band method was then performed for combining the mooring line tension ranges， and the fatigue damage of mooring lines was estimated by both S-N curves and fracture mechanics based approaches. A comparison between S-N curves based fatigue assessment approaches and the developed fracture mechanics based mooring fatigue assessment approach was made， and the results showed that fatigue lives estimated by these two approaches were generally comparable if the safety factors suggested by DNV were applied to S-N curves based approaches. The developed fracture mechanics based mooring fatigue assessment approach was then applied for mooring chain links subjected to out-of-plane bending （OPB）. The result showed that the fatigue life of mooring chains on 5， 7 and 9 pocket sprockets affected by out-of-plane bending was reduced by 19%， 11% and 9% respectively.