In recent years, the problem of rogue waves has been a topical issue among oceanographers because of their dangerous and unpredictable properties, leading to safety demands for ships and offshore platforms. Even with efforts to physically quantify the mechanism of rogue wave generation within the last two decades, rogue wave events are still unpredictable, as the rogue wave mechanism has not yet been fully explained, both mathematically and physically. This study investigates whether a Lax–Wendroff method-based algorithm with the wave action equation can characterise a 2-dimensional regular wave group over deep water. The Lax–Wendroff method up to a second-order approximation was applied to the wave action equation and the formulated algorithm was validated by means of experimental data, which consisted of a measured local regular wave group (wave frequency: 1.6 Hz, wave amplitude: 0.54 cm). The model consists of a computational algorithm which can describe a spatial evolution of wave frequencies (radian frequencies) and envelopes in the time domain with second-order accuracy, when the initial values at the first position are provided. As a result, the Lax–Wendroff method-based algorithm characterised an evolution of the regular wave group up to 4.5 m, implying that the Lax–Wendroff method-based algorithm could be a promising mathematical formulation in the understanding and characterisation of rogue wave formation, providing a further insight into a linear focusing mechanism. In the future, the results of this study will be extended to investigate the validity of the Lax–Wendroff method-based algorithm in finite water depth.