Considering the limitations of low and extended trajectory and short terminal trajectory on laser terminal guidance of range extend individual rocket, the target acquisition domain and target acquisition probability of the strapdown laser guidance seeker in the whole terminal trajectory were researched. A model of target acquisition domain for semi-active laser seeker in low and extended trajectory was established. The target acquisition domain and the minimum cone field of the seeker in the whole terminal trajectory were simulated under the condition of different rocket fire angles. The position in terminal trajectory and the minimum half field angle when target acquisition domain boundary changing from hyperbolic to ellipse were analyzed, and the optimum half field angle was 5.9°. Considering the influence of trajectory disturbance, the target acquisition probability of the seeker at different positions in terminal trajectory were calculated, and the optimum initial detection point of missile seeker in terminal trajectory was established by means of Monte Carlo method. The limitations of low and extended trajectory and short terminal trajectory on laser terminal guidance of individual rocket were solved. The reference for guidance of the extended range rocket projectile was provided.