We present an X-band high-power pulse compression system for a klystron-based compact linear collider. In this system design, one rf power unit comprises two klystrons, a correction cavity chain, and two SLAC Energy Doubler (SLED)-type X-band pulse compressors (SLEDX). An rf pulse passes the correction cavity chain, by which the pulse shape is modified. The rf pulse is then equally split into two ways, each deploying a SLEDX to compress the rf power. Each SLEDX produces a short pulse with a length of 244 ns and a peak power of 217 MW to power four accelerating structures. With the help of phaseto-amplitude modulation, the pulse has a dedicated shape to compensate for the beam loading effect in accelerating structures. The layout of this system and the rf design and parameters of the new pulse compressor are described in this work.