Preventing the formation of brittle intermetallic compounds and defects or porosity in the fusion zone is a major challenge when welding dissimilar materials. Additionally, differences of physical properties between two joined materials generate thermal expansion mismatch stresses on cooling which means these weaknesses can quickly lead to failure. Welding research has not yet fully overcome these problems. In this study, Ti-6Al-4V titanium alloy and Inconel 718 nickel alloy are joined together using an IPG 1 kW single mode fibre laser and each sample evaluated in terms of the extent of the fusion and heat affected zones, and their microstructures. The effects of the process parameters of laser power, welding speed, focal position of the laser beam and beam offset from the centre of the bond on the samples are evaluated. It is found that narrow full depth welds can be obtained but the formation of cracks within them cannot be controlled by changing the laser power, traverse speed or focal position of the laser beam. Shifting the beam from the bonding line to the Ti-6Al-4V alloy side proves a successful method of eliminating visible signs of cracking.