Owing to its generality and efficiency, Cascaded Shadow Maps (CSMs) has an important role in real-time shadow rendering in large scale and complex virtual environments. However, CSMs suffers from redundant rendering problem --objects are rendered undesirably to different shadow map textures when view direction and light direction are not perpendicular. In this paper, we present a light space cascaded shadow maps algorithm. The algorithm splits a scene into non-intersecting layers in light space, and generates one shadow map for each layer through irregular frustum clipping and scene organization, ensuring that any shadow sample point never appears in multiple shadow maps. A succinct shadow determination method is given to choose the optimal shadow map when rendering scenes. We also combine the algorithm with stable cascaded shadow maps and soft shadow algorithm to avoid shadow flicking and produce soft shadows. The results show that the algorithm effectively improves the efficiency and shadow quality of CSMs by avoiding redundant rendering, and can produce high-quality shadow rendering in large scale dynamic environments with real-time performance.