A vehicle start control device, wherein in the vehicle an output of an engine is output to a transmission via a torque converter having a lock-up clutch, the device comprising: a start request detection unit adapted to detect a start request for the vehicle; a hydraulic pressure control circuit adapted to control a torque transmittable by the lock-up clutch by controlling an engagement force of the lock-up clutch in response to the start request for the vehicle; and a control unit adapted to instruct the hydraulic pressure control circuit to perform a slip control for the lock-up clutch during a vehicle start, wherein the control unit has a rotation speed obtaining unit adapted to obtain an engine rotation speed (Ne) of the engine at a corresponding timing, a target rotation speed computing unit adapted to compute a target rotation speed (tNe) of the engine in the slip control at a corresponding timing, a control target value computing unit adapted to compute a control target value, which is a target value necessary in an immediately following control cycle to control the engine rotation speed (Ne) to the target rotation speed (tNe) based on the engine rotation speed (Ne) and the target rotation speed (tNe), and an instruction value computing unit adapted to compute an instruction value for an engagement force of the lock-up clutch necessary to control the engine rotation speed (Ne) to the control target value in an immediately following control cycle, Wherein the instruction value computing unit is adapted to compute the instruction value for the engagement force of the lock-up clutch based on the engine rotation speed at a corresponding timing and the control target value of an immediately following control cycle. a start request detection unit adapted to detect a start request for the vehicle; a hydraulic pressure control circuit adapted to control a torque transmittable by the lock-up clutch by controlling an engagement force of the lock-up clutch in response to the start request for the vehicle; and a control unit adapted to instruct the hydraulic pressure control circuit to perform a slip control for the lock-up clutch during a vehicle start, wherein the control unit has a rotation speed obtaining unit adapted to obtain an engine rotation speed (Ne) of the engine at a corresponding timing, a target rotation speed computing unit adapted to compute a target rotation speed (tNe) of the engine in the slip control at a corresponding timing, a control target value computing unit adapted to compute a control target value, which is a target value necessary in an immediately following control cycle to control the engine rotation speed (Ne) to the target rotation speed (tNe) based on the engine rotation speed (Ne) and the target rotation speed (tNe), and an instruction value computing unit adapted to compute an instruction value for an engagement force of the lock-up clutch necessary to control the engine rotation speed (Ne) to the control target value in an immediately following control cycle, Wherein the instruction value computing unit is adapted to compute the instruction value for the engagement force of the lock-up clutch based on the engine rotation speed at a corresponding timing and the control target value of an immediately following control cycle.