Laser drilling has become an alternative to drilling precise holes in advanced difficult-to-cut superalloys. Due to better hole quality and capability to generate macro-size holes, laser trepan drilling is becoming more popular as compared with laser percussion drilling. This paper presents a study of laser trepan drilling process performance in terms of geometrical quality characteristics, such as hole taper and circularity for drilling small diameter hole in difficult-to-cut Titanium alloy sheet. Due to involvement of different process parameters such as laser power, pulse width, pulse frequency, workpiece thickness, material composition, cutting speed, stand of distance and assist gas pressure, the laser cutting is a highly nonlinear and complex process. To handle this nonlinearity and complexity, genetic algorithm has been applied for the optimization. We used assist gas pressure, pulse width, pulse frequency and trepanning speed as input process parameters. The effect of significant process parameters on hole characteristics are discussed on the basis of data obtained through a well designed orthogonal array experimental matrix. Reliable empirical models have been developed for different quality characteristics. Improvements of 49% and 8% have been registered in hole taper and circularity, respectively, at optimum level of process parameters.