A vehicle control apparatus provided with an internal combustion engine having an output shaft and a rotary electric machine (MG1, MG2) each functioning as a power source, and operative in states changeable between a stopped state and an operation state of the internal combustion engine while a vehicle is running, comprising: an internal combustion engine starting unit that rotates the output shaft of the internal combustion engine with the power of the rotary electric machine (MG1, MG2) in response to an acceleration request to execute a start-up control to have the internal combustion engine transferred from the stopped state to the operation state, and a rise rate setting unit that sets a rise rate of an engine rotational speed of the internal combustion engine after a completion of the start-up operation, wherein the rise rate setting unit being operative to set the rise rate of the engine rotational speed of the internal combustion engine to a higher rise rate in a case that a condition is established with a vehicle speed higher than a predetermined vehicle speed value, and with a value indicative of the acceleration request higher than a predetermined value, which is not zero, as compared with a normal rise rate which is set in a case that the condition is not established with the vehicle speed higher than the predetermined vehicle speed value, and with the value indicative of the acceleration request higher than the predetermined value, which is not zero, characterized in that the rise rate setting unit is operative to reduce the rise rate setting of the engine rotational speed by a reduction value, which is smaller than a difference between the higher rise rate and the normal rise rate, if an actual rise rate is increased beyond the higher rise rate within a predetermined time period after the completion of the start-up operation, and to set the rise rate of the engine rotational speed to the higher rise rate after elapse of said time period. an internal combustion engine starting unit that rotates the output shaft of the internal combustion engine with the power of the rotary electric machine (MG1, MG2) in response to an acceleration request to execute a start-up control to have the internal combustion engine transferred from the stopped state to the operation state, and a rise rate setting unit that sets a rise rate of an engine rotational speed of the internal combustion engine after a completion of the start-up operation, wherein the rise rate setting unit being operative to set the rise rate of the engine rotational speed of the internal combustion engine to a higher rise rate in a case that a condition is established with a vehicle speed higher than a predetermined vehicle speed value, and with a value indicative of the acceleration request higher than a predetermined value, which is not zero, as compared with a normal rise rate which is set in a case that the condition is not established with the vehicle speed higher than the predetermined vehicle speed value, and with the value indicative of the acceleration request higher than the predetermined value, which is not zero, characterized in that the rise rate setting unit is operative to reduce the rise rate setting of the engine rotational speed by a reduction value, which is smaller than a difference between the higher rise rate and the normal rise rate, if an actual rise rate is increased beyond the higher rise rate within a predetermined time period after the completion of the start-up operation, and to set the rise rate of the engine rotational speed to the higher rise rate after elapse of said time period.