This paper reports a statistical analysis of the laser wood cutting process. The laser cutting of wood is a multi-factor process and correct combination of the parameters involved is needed to achieve high quality and optimum process efficiency. In this paper a design of experiments and statistical modelling approach is used to investigate the significant process parameters by consideration of parameter interactions. A high brightness, 1 kW IPG single mode ytterbium-doped fibre laser was used to cut dry pine wood samples. The investigated parameters include laser power, focal plane position, traverse speed, gas pressure, number of passes, and cutting direction. Results are compared against a number of response factors defining the process efficiency (i.e. kerf depth, mass removal, and specific energy consumption) and the cut quality (i.e. heat-affected zone, kerf width, and edge surface roughness). It is reported that the majority of these process characteristics are significantly affected by the structure of the wood under test.