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By using the generalized static replica symmetry approximation, the quantum XY spin-glass model in a longitudinal field is investigated. The thermodynamic quantities, spin-glass and self-interaction order parametersare calculated numerically. The local susceptibility depending on temperature has the typical spin-glass plateaucharacteristic; the specific heat against temperature display a crossover feature which was discovered experimentally in the CuMn sample by Brodale et al. (J. Magn. Magn. Mater. 31-34 (1983) 1331) and cusps sharperthan that in the model with the Dzyaloshinskii-Moriya interaction.