Studied in this paper are the bright-dark vector soliton solutions for a generalized coupled Hirota system which describes the propagation for the high-intensity ultrashort pulses in the optical glass fiber. Beyond the existing bilinear forms, using an auxiliary function, we obtain the improved bilinear forms and bright-dark soliton solutions under two integrable constraints through the Hirota method and symbolic computation. With the help the analytic and graphic analysis, we study the soliton properties including the amplitudes, velocities and phase shifts, and show that the interactions for the bright-dark two solitons are elastic. For the bright-dark one soliton, parametric conditions that the dark component is "black" or "gray" are obtained. For the bright-dark two solitons, we find that the bright component is affected by the dark component background parameters during such an interaction, while the dark component is not affected by the bright component background parameters. Velocities for the bright-dark two solitons are inversely proportional to the higher-order effect parameter, but amplitudes and phase shifts are independent of it. Besides, the bound-state bright-dark two solitons are also presented. (C) 2016 Elsevier B.V. All rights reserved.