Abstract Laser transmission welding involves localized heating and non-contact techniques at the interface of two polymer pieces to be joined. The welding quality is very sensitive to speed welding, thickness and welding line width and depth. This work presents the laser transmission welding of Poly(Methyl Meta acrylate) PMMA polymer transparent and oblique slabs. A semiconductor laser with 808 nm wavelength, 2 W output power and a 2 mm beam diameter was used. Three different transparent slabs with dimensions 40 × 60 mm and thickness (2.6, 3.7, 4.3 mm) were fixed tightly onto oblique slab (dark color). Three different selected speeds (44, 113, 150 mm/min) of the welding process were applied to the prepared samples. Results indicate the welding line width and depth were inversely proportional to the welding speed while the transparent slab thickness have little effect. Nine experiments were performed for the three different thickness at different speeds. Taguchi method and grey relational analysis were used to determine the optimum values for welding speed, width, depth and thickness during these nine experiments. The results exhibit good agreement with those of the Taguchi method and grey relational analysis.