Laser additive manufacturing (LAM) is based on selectively adding materials, layer by layer, to form a 3D part using one or multiple laser beams to fuse or solidify the materials. Although considerable amount of work can be found on investigating the LAM processes, little is known on the effects of gravity and dynamic fluid flow characteristics in different material growth orientations. Along with the advancement of laser manufacturing techniques, LAM is increasingly being used in a wide variety of environments including cylinder body, surface cladding on turbine blades, offshore drilling heads, and side walls of sleeve and mould where various deposition orientations are normally required. In addition, for space additive manufacturing, the operating environment will experience very low or zero gravity. Many efforts have been made by the previous research on developing numerical methods to model the LAM process. However, most of the previous modelling work has been focusing on development of the melt pool dynamics without taking into account of the free surface formation. Only a few investigations include the analysis of material addition into the dynamic flowing melt pool. No work has been found on developing a model which can simulate the deposition process with all complex features and taking gravity effects into consideration when performed in various material deposition orientations and zero gravity effects. In this research, a three-dimensional transient computational fluid dynamic model was built for the LAM process which took into account compound process factors including material addition, surface tension, melting and solidification, gravitational force, temperature dependent material properties, free surface formation and moving heat source. A better understanding of laser metal deposition process was achieved numerically and experimentally. The research covered the deposition of single layer, multiple adjacent passes and full three-dimensional geometries with overhanging features. Effects of gravity during the deposition process in various deposition orientations and for zero gravity and very low gravity were investigated and process parameters were optimised to minimise the effect. The research also extended to understanding of basic phenomena in a laser narrow gap welding process, based on layer by layer material addition, and how gravity would affect the melt pool formation inside the groove when the welding process was performed in different orientations. By analysing the melt pool development history and temperature distribution, the influence of surface tension coefficient was discussed during the process. With the help of the current model, various defects including deposition irregularity, bulge and slope at both ends of the deposition, lack of fusion, step effect, surface waviness and collapsing as a result of change of gravity were explained. Corresponding solutions to eliminate all these defects were presented. The work on zero-gravity laser additive manufacturing discovered several new phenomena not reported before, paving the way for future laser 3D printing in space.