A hydraulic pressure control apparatus of a construction machine, comprising: a hydraulic pump (11, 12); first and second control valve units configured to control a flow direction of a working fluid discharged from the hydraulic pump (11, 12) to supply the working fluid to first and second working tools, respectively, and to control opening degrees of passages connecting the first and second working tools and the hydraulic pump (11, 12), respectively; and a control unit configured to control the first and second control valve units in response to manipulation signals input from first and second manipulating parts, respectively, wherein the control unit determines whether a current working mode is a general working mode or a prior working mode corresponding to a prior driving actuator performing a prior function, when it is determined that the current working mode is a general working mode, calculates a first normal passage opening degree in response to a manipulation signal input from the first manipulating part to output the first normal passage opening degree to the first control valve unit, and calculates a second normal passage opening degree in response to a manipulation signal input from the second manipulating part to output the second normal passage opening degree to the second control valve unit, and when it is determined that the current working mode is a prior working mode, outputs a control signal to the second control valve unit so that an opening degree of the second control valve unit becomes smaller than the first normal passage opening degree such that an amount of the working fluid supplied to the first working tool is secured first. a hydraulic pump (11, 12); first and second control valve units configured to control a flow direction of a working fluid discharged from the hydraulic pump (11, 12) to supply the working fluid to first and second working tools, respectively, and to control opening degrees of passages connecting the first and second working tools and the hydraulic pump (11, 12), respectively; and a control unit configured to control the first and second control valve units in response to manipulation signals input from first and second manipulating parts, respectively, wherein the control unit determines whether a current working mode is a general working mode or a prior working mode corresponding to a prior driving actuator performing a prior function, when it is determined that the current working mode is a general working mode, calculates a first normal passage opening degree in response to a manipulation signal input from the first manipulating part to output the first normal passage opening degree to the first control valve unit, and calculates a second normal passage opening degree in response to a manipulation signal input from the second manipulating part to output the second normal passage opening degree to the second control valve unit, and when it is determined that the current working mode is a prior working mode, outputs a control signal to the second control valve unit so that an opening degree of the second control valve unit becomes smaller than the first normal passage opening degree such that an amount of the working fluid supplied to the first working tool is secured first.