In this paper, a compact cat swarm optimization algorithm based on a Small Sample Probability Model (SSPCCSO) is proposed. In the same way as with previous algorithms, there is a tracking mode and a searching mode in the processing of searching for optimal solutions, but besides these, a novel differential operator is introduced in the searching mode, and it is proved that this could greatly enhance the search ability for the potential global best solution. Another highlight of this algorithm is that the gradient descent method is adopted to increase the convergence velocity and reduce the computation cost. More importantly, a small sample probability model is designed to represent the population of samples instead of the normal probability distribution. This representation method could run with low computing power of the equipment, and the whole algorithm only uses a cat with no historical position and velocity. Therefore, it is suitable for solving optimization problems with limited hardware. In the experiment, SSPCCSO is superior to other compact evolutionary algorithms in most benchmark functions and can also perform well compared to some population-based evolutionary algorithms. It provides a new means of solving small sample optimization problems.