A boom driving apparatus for a construction machine, the apparatus being provided in the construction machine including a base machine and a working attachment, the working attachment having a boom attached to the base machine so as to be able to be raised and lowered, and an arm pivotably coupled to a tip of the boom, to hydraulically drive the boom, the apparatus comprising: a boom cylinder interposed between the base machine and the boom and connected to the boom and to the base machine so as to actuate the boom in a raising direction with an extension of the boom cylinder; a variable-displacement hydraulic pump which sucks hydraulic oil stored in a tank and discharges the hydraulic oil; a boom control valve switchable between a position for leading hydraulic oil discharged by the hydraulic pump to a head-side chamber of the boom cylinder to extend the boom cylinder and a position for leading hydraulic oil discharged by the hydraulic pump to a rod-side chamber of the boom cylinder to contract the boom cylinder; a boom-raising-operation detector which detects that a boom raising operation for actuating the boom in the raising direction is being applied to the boom control valve; a boom-cylinder pressure detector which detects a pressure in at least the rod-side chamber of the boom cylinder out of the head-side chamber and the rod-side chamber of the boom cylinder; a supply selector valve switchable between a permission position for permitting hydraulic oil to be supplied from the hydraulic pump to the head-side chamber of the boom cylinder and a blocking position for blocking the supply of hydraulic oil from the hydraulic pump to the head-side chamber; a supply oil passage which brings the tank and the head-side chamber of the boom cylinder into communication with each other so as to permit hydraulic oil to be supplied from the tank to the head-side chamber when the supply selector valve blocks the supply of the hydraulic oil; characterized by a controller which brings the supply selector valve into the blocking position and makes volume of the hydraulic pump smaller than volume of the hydraulic pump when the supply selector valve is in the permitting position, only in the case where the boom-raising-operation detector detects the boom raising operation and the pressure detected by the boom-cylinder pressure detector satisfies an extension permission condition which is preset up to judge a state where an excavation reaction force exerted on the working attachment is being sufficient to extend the boom cylinder even with no supply of the hydraulic oil from the hydraulic pump to the head-side chamber of the boom cylinder. a boom cylinder interposed between the base machine and the boom and connected to the boom and to the base machine so as to actuate the boom in a raising direction with an extension of the boom cylinder; a variable-displacement hydraulic pump which sucks hydraulic oil stored in a tank and discharges the hydraulic oil; a boom control valve switchable between a position for leading hydraulic oil discharged by the hydraulic pump to a head-side chamber of the boom cylinder to extend the boom cylinder and a position for leading hydraulic oil discharged by the hydraulic pump to a rod-side chamber of the boom cylinder to contract the boom cylinder; a boom-raising-operation detector which detects that a boom raising operation for actuating the boom in the raising direction is being applied to the boom control valve; a boom-cylinder pressure detector which detects a pressure in at least the rod-side chamber of the boom cylinder out of the head-side chamber and the rod-side chamber of the boom cylinder; a supply selector valve switchable between a permission position for permitting hydraulic oil to be supplied from the hydraulic pump to the head-side chamber of the boom cylinder and a blocking position for blocking the supply of hydraulic oil from the hydraulic pump to the head-side chamber; a supply oil passage which brings the tank and the head-side chamber of the boom cylinder into communication with each other so as to permit hydraulic oil to be supplied from the tank to the head-side chamber when the supply selector valve blocks the supply of the hydraulic oil; characterized by a controller which brings the supply selector valve into the blocking position and makes volume of the hydraulic pump smaller than volume of the hydraulic pump when the supply selector valve is in the permitting position, only in the case where the boom-raising-operation detector detects the boom raising operation and the pressure detected by the boom-cylinder pressure detector satisfies an extension permission condition which is preset up to judge a state where an excavation reaction force exerted on the working attachment is being sufficient to extend the boom cylinder even with no supply of the hydraulic oil from the hydraulic pump to the head-side chamber of the boom cylinder.