External cavity tunable semiconductor lasers have wide applications in fiber sensing, cold atom physics, laser radar, etc. To achieve wide mode-hopping free tuning range, the length of laser cavity, parameter of grating, the position of optical elements in the cavity and the position of pivot point should be carefully designed. The Littman-Metcalf type external cavity tunable semiconductor laser is modeled to study the longitudinal allowanceerror for mode-hopping free tuning. The influence of the distance from pivot point to motion axis of piezoelectric ce.ramic motor and the diffracting point of the blazed grating, the installation angle of the blazed grating, and the grat.ing groove density are analyzed. The results show that mode-hopping can be effectively avoided with careful choos. ing the parameters above.