Electrostatic sensors have been widely used in many applications due to their advantages of low cost and robustness. Their spatial sensitivity and time-frequency characteristics are two important performance parameters. In this paper, an analytical model of the induced charge on a novel hemisphere-shaped electrostatic sensor was presented to investigate its accurate sensing characteristics. Firstly a Poisson model was built for electric fields produced by charged particles. Then the spatial sensitivity and time-frequency response functions were directly derived by the Green function. Finally, numerical calculations were done to validate the theoretical results. The results demonstrate that the hemisphere-shaped sensors have highly 3D-symmetrical spatial sensitivity expressed in terms of elementary function, and the spatial sensitivity is higher and less homogeneous near the hemispherical surface and vice versa. Additionally, the whole monitoring system, consisting of an electrostatic probe and a signal conditioner circuit, acts as a band-pass filter. The time-frequency characteristics depend strongly on the spatial position and velocity of the charged particle, the radius of the probe as well as the equivalent resistance and capacitance of the circuit.