Nowadays the long-range dipole-dipole interaction between highly-excited Rydberg atoms at micrometer distance become promising way to establish the atom-atom quantum entanglement and to implement the two-qubit logic gate. For alkali metal atoms, single-photon excitation from the ground state to the desired Rydberg state demands powerful narrow-linewidth ultra-violet (UV) laser, which is very challenging. Maybe just because of this, the studies of single-photon Rydberg excitation of alkali metal atoms are rare. Alternatively people have employed the two-photon or three-photon Rydberg excitation scheme. However, comparing with the single-photon Rydberg excitation, the two-photon or three-photon scheme has following drawbacks: atomic decoherence due to the photon scattering from the lower and upper transitions, and light shift of the involved ground state and Rydberg state due to the lower and upper transition laser beams. Thanks to the efficient laser frequency conversion technology with PPXX material and the well-developed commercial fiber laser as well as fiber amplifier, we have implemented a tunable 318.6-nm UV laser system based on the cavity-enhanced second-harmonic generation following the single-pass sum-frequency generation of 1560.5-nm and 1076.9-nm fiber-amplified lasers. More than 2-Watt output of the 318.6-nm UV laser has been achieved with a typical linewidth of smaller than 10 kHz. Employing the UV laser system we have demonstrated a single-photon Rydberg excitation spectroscopy of cesium (Cs) atoms. Partial Cs atoms can be directly excited from 6S_1/2 ground state to nP_3/2 (n = 70 - 100) Rydberg states, and Rydberg excitation spectra are obtained with transmission enhancement of a probe beam locked to Cs 6S_1/2 (F = 4) - 6P_3/2 (F’ = 5) cycling transition because partial population on the ground state (F = 4) are transferred to Rydberg state. The quantum defect for Cs nP_3/2 (n = 70 -100) Rydberg states is determined experimentally. Further more, the demodulated single-photon Rydberg excitation spectrum is employed to stabilize the UV laser to specific Cs Rydberg transition to improve the laser frequency stability. References:  Opt. Express 25 (2017) p.22510;  J. Opt. 19 (2017) 045501;  J. Opt. Soc. Am. B 33 (2016) p.2020;  Opt. Commun. 370 (2016) p.150. Funding: the National Natural Science Foundation of China (61475091).