A method of studying a non-equilibrium x-ray laser plasma is developed by extending the existing one-dimensional similarity equations to the case of two-dimensional plasma study in the directions perpendicular to the slab and along a focal line. With this method the characteristics of pre-plasma are optimized for transient neon-like Cr x-ray laser. It is found that when the duration and the intensity of 1.053 μm pre-pulse are 1.2 ns and 6.5 TW/cm2respectively with a delay time of 1.5 us, the temperature and the temperature discrepancy each approach a proper state, which will provide a uniform distribution of properly ionized neon-like Cr ions before the arrival of pumping pulse.