Multi-mode high-spectral-resolution lidar is a new concept of high-spectral-resolution lidar, which uses the multiple-longitudinal-mode pulsed laser rather than the single frequency laser. In this paper, we analyze the multiple longitudinal mode and its spectral distribution of a typical Nd:YAG laser, and calculate its corresponding Mie scattering and Rayleigh scattering spectra, which are a convolution between the spectral distribution of multiple-longitudinal-mode laser pulse and that of the Mie and Rayleigh scattering excited by a single frequency laser pulse. According to the spectral analyses of the elastic lidar returns, we design an ultraviolet multi-mode high-spectral-resolution lidar, in which a high-power non-seeded Nd:YAG pulsed laser at the third harmonic 355 nm wavelength is used as a transmitter, and a Cassegrain telescope serves as a receiver. In the polychromator, a narrow band interfering filter is selected to block the solar background, and a tunable Mach-Zehnder interferometer (MZI) is designed to separate the aerosol Mie scattering signals from the molecular Rayleigh scattering signals excited by the multi-mode pulsed laser. The MZI is composed of a roof mirror mounted on a piezoelectric ceramic and two beam splitters. The optical path difference of the MZI can be adjusted by the piezoelectric ceramic, while its optimum value should make the correspondence between the free spectral range of MZI and the interval between longitudinal modes of Nd:YAG pulsed laser. The photomultiplier tube is selected as a detector, whose output is the convolution between the transmission function of MZI and the Mie and Rayleigh signals excited by the multi-longitudinal mode laser pulse. In the practical experiment, the optimal optical path difference of MZI can be determined by using envelope analysis. For the transmitter laser, when one channel has a maximum output signal and the other has a minimum output, the center wavelength of each longitudinal mode of laser is locked in the optimal optical path difference. The channel of MZI with the maximum output is to pass the Mie scattering signal, while the channel with the minimum output is to block the Mie scattering signal. The aerosol optical characteristics are retrievable by using the complementary properties of the two output channels of MZI. In order to verify the feasibility of the multi-mode high spectral resolution lidar, the system simulation is carried out by using the real atmospheric model and the designed lidar system parameters. The simulation results show that the designed ultraviolet multi-mode high-spectral-resolution lidar can realize the accurate measurement of aerosol within a height of 10 km.