Selenium cluster cations are produced by the combination of laser vaporization and supersonic expansion techniques. Each small cluster cation Se-n(+) (n=3-8) is mass selected separately and subjected to one-photon laser photodissociation processes. The parent and daughter cluster ions are detected using a reflectron time-of-flight mass spectrometer. The appearance potentials of all the observed cluster fragment ions are estimated from their yield curves as a function of the laser wavelength. The neutral dimer evaporation is found to be the lowest energy photodissociation channel. In general, the odd-numbered cluster cations have much larger dissociation thresholds than those of the even-numbered cluster cations. In addition, the dissociation thresholds of the odd-numbered cations decrease with the increasing cluster size, while those of the even-numbered clusters increase with the increasing cluster size. A sequential neutral dimer evaporation mechanism is demonstrated in the photodissociation of some cluster cations at high photon energies.