The article introduces a new compact cesium beam clock with a non-uniform magnetic field for state selection and a laser that resonates with D2 4-5 line for detection. The basic structure which contains the physical system, the optical system, and the servo system as well as the operation principle of the clock, is described. A 4U size prototype with stability of 4. 0×10 -13@ 100 s, 4. 5×10 -14@ 10 000 s and 2. 2×10 -14@ 1 d is realized, which is better than high performance type 5071A cesium beam clock. The clock is compared with the conventional cesium beam clock and the optically pumped cesium beam clock. The advantages and disadvantages of the clock are analyzed. Two feasible improved schemes are introduced, which are expected to further improve the stability to better than 3×10 -13@ 100 s. One scheme uses a laser that resonates with D2 3-2 line for detection. The other scheme uses optical pumping and non-uniform magnetic field together for state preparation.