A novel fan-shaped ray-leakage-free solar concentrator is proposed. The relation of geometrical concentration ratio with parabola coefficient, posterior paraboloid width of concentration module and concentration module quantity is also explored. The proposed design method of the sawtooth ray-leakage-free lightguide can deal with the leaking situation after the coupling inlets array, which increases the optical efficiency and the concentration ratio. By the analysis of the sun tracking law, a single-axis tracker with the scrollable prism sheets is proposed instead of double-axes tracker, which can decrease the system power dissipation. The ray-tracing simulations are carried out by LightTools software considering the Fresnel loss and optical material absorption. The results show that the concentration ratio and optical efficiency are 1900 and 65.1% when the parabola coefficient is 0.019; the concentration ratio and optical efficiency are 1110 and 82.3% when the parabola coefficient is 0.032.