In this paper the physical model and numerical algorithm of particle-in-cell (PIC) simulation for gas-puff Z-pinch in two-dimensional cylindrical coordinates are briefly introduced. The code is also developed according to the model and algorithm. The rarefied gas-puff Z-pinch driven by a low current is simulated through the code, and some reasonable results are obtained. The results include the spatiotemporal distributions of current, electromagnetic field, particle positions and density, as well as the trailing mass and current. It is found that the simulated current reflects the plasma Z-pinch characteristics, i.e., the plasma current arrives at a minimum when the plasma enters into stagnation, and it begins to increase after the plasma has moved outwards. The simulated magnetic field agrees well with the theoretic value. The electric field force and magnetic field force experienced by electron are almost the same in magnitude, while the force acting on ion is mainly the electric field force. Firstly the electron is accelerated in the z direction and reaches a velocity, then it moves inward the axis in the same time by the Lorentz force. That causes the separation between electron and ion, and a strong electric field is produced. The produced electric field attracts the ion inward the electron. When the electrons arrive at the axis, they move inversely due to the static repellency among them, while the ions continue to move initially inwards, and later enter into stagnation, and finally collapse. The trailing mass is about 20% of the total Z-pinch plasma, and the maximum trailing current is about 7% of the driven current. In the future the code needs to develop further and realize parallel computation in order to simulate the practical Z-pinch processes by PIC simulation.