We have applied a dual-pulse laser-induced breakdown spectroscopy (DP-LIBS) to sensitively detect concentrations of boron and lithium in aqueous solution. Sequential laser pulses from two separate Q-switched Nd:YAG lasers at 532 nm wavelength have been employed to generate laser-induced plasma on a water jet. For achieving sensitive elemental detection, the optimal timing between two laser pulses was investigated. The optimum time delay between two laser pulses for the B atomic emission lines was found to be less than 3 μs and approximately 10 μs for the Li atomic emission line. Under these optimized conditions, the detection limit was attained in the range of 0.8 ppm for boron and 0.8 ppb for lithium. In particular, the sensitivity for detecting boron by excitation of laminar liquid jet was found to be excellent by nearly 2 orders of magnitude compared with 80 ppm reported in the literature. These sensitivities of laser-induced breakdown spectroscopy are very practical for the online elemental analysis of boric acid and lithium hydroxide serving as neutron absorber and pH controller in the primary coolant water of pressurized water reactors, respectively.