Superconducting properties of novel BiSe$_{2}$-based layered LaO$_{1-x}$F$_{x}$BiSe$_{2}$ single crystals

F-doped LaOBiSe$_{2}$ superconducting single crystals with typical size of 2$times$4$times$0.2 mm$^{3}$ are successfully grown by flux method and the superconducting properties are studied. Both the superconducting transition temperature and the shielding volume fraction are effectively improved with fluorine doping. The LaO$_{0.48}$F$_{0.52}$BiSe$_{1.93}$ sample exhibits zero-resistivity at 3.7 K, which is higher than that of the LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$ polycrystalline sample (2.4K). Bulk superconductivity is confirmed by a clear specific-heat jump at the associated temperature. The samples exhibit strong anisotropy and the anisotropy parameter is about 30, as estimated by the upper critical field and effective mass model