This study focuses on experimental investigation, predictive modeling, and process optimization in Nd-YAG laser microgrooving operation of titanium alloy (Ti6Al4V) by considering diode current, pulse frequency, scan speed, and the number of passes as process parameters. The technological response characteristics in the laser microgrooving process such as upper width, depth, and heat-affected zone have been considered to assess the machining performances. Thirty-one sets of laser microgrooving trials based on the design of experiment (DOEs) are performed along with analysis of variance (ANOVA), response surface methodology (RSM), and particle swarm optimization (PSO) that are subsequently applied for parametric influence study, mathematical modeling and multi-response optimization, respectively. Results indicated that groove width and HAZ decrease with a lower magnitude of diode current but opposite trend occurs with scan speed and the groove depth increases with the increase of pulse frequency. From the pre-cited parameters, the number of passes is found to be the most significant parameter that affects almost all quality characteristics. By solving the optimization problem with PSO, corresponds to the optimal setting of process parameters (diode current = 24.5 amp, pulse frequency = 29.36 kHz, scan speed = 40 mm/s, number of passes = 9) with estimated upper width 0.0596 mm, heat-affected zone 0.1303 mm, and depth 0.3966 mm. © Springer Nature Singapore Pte Ltd. 2019.