On the days prior to the genesis of Graham the inter-tropical convergence zone was located near latitude 15°S across northern Australia. A low became evident just south of this zone on 27 January. It moved eastward and deepened reaching cyclonic intensity just before it crossed the coast at about 0000 UTC on the 28th. The cyclone then weakened into a rain bearing depression as it moved inland. During the 29th it recurved to the west as a ridge of high pressure developed to the south.
At 0000 UTC on the 31st the system moved out to sea and redeveloped rapidly. It subsequently moved to the southwest and approached the coast again. Maximum intensity occurred just before this second landfall when the central pressure was estimated at 980 hPa and winds of 100 km/h were expected near the centre. At 2325 UTC on the 31st the cyclone passed about 25 km south of Port Hedland and winds of 81 km/h with gusts up to 119 km/h were recorded. This wind was the strongest reported during the life of Graham .
During 28, 29 and 30 January Graham caused extensive rainfall over the Kimberley, with 24-hour totals of over 100 mm being common. The highest 24-hour rainfall was 178 mm at Broome for the period ending 0100 UTC 30 January. Pardoo station reported some building damage and the loss of many trees.