A control apparatus for a transmission of a vehicle, the transmission including a continuously variable transmission mechanism including an input-side pulley, an output-side pulley and a belt, the belt being wound to span between the input-side pulley and the output-side pulley, a gear mechanism including one or a plurality of gear stages, the continuously variable transmission mechanism and the gear mechanism being provided in parallel with each other between an input rotating member and an output rotating member, power of a driving force source being transmitted to the input rotating member, the output rotating member being configured to output the power to a drive wheel, and a clutch mechanism (C1, C2, B1) configured to selectively change a power transmission path between a first path and a second path, the first path being a path through which the power of the driving force source is transmitted via the continuously variable transmission mechanism, the second path being a path through which the power of the driving force source is transmitted via the gear mechanism, the clutch mechanism including a clutch configured to transmit power or interrupt transmission of power in the second path, the control apparatus comprising: an electronic control unit configured to i) when at least one of an input pulley hydraulic pressure (Pin) applied to the input-side pulley or an output pulley hydraulic pressure (Pout) applied to the output-side pulley is larger than a clutch hydraulic pressure applied to the clutch while the clutch is engaged and the power of the driving force source is transmitted through the second path, control the at least one of the input pulley hydraulic pressure or the output pulley hydraulic pressure larger than the clutch hydraulic pressure such that a winding radius of the belt on the at least one of the input-side pulley or the output-side pulley, to which a hydraulic pressure larger than the clutch hydraulic pressure is applied, decreases, and ii) when the clutch hydraulic pressure is larger than any of the input pulley hydraulic pressure (Pin) and the output pulley hydraulic pressure (Pout), control the input pulley hydraulic pressure and the output pulley hydraulic pressure such that a winding radius of the belt on the input-side pulley decreases and a winding radius of the belt on the output-side pulley increases. i) when at least one of an input pulley hydraulic pressure (Pin) applied to the input-side pulley or an output pulley hydraulic pressure (Pout) applied to the output-side pulley is larger than a clutch hydraulic pressure applied to the clutch while the clutch is engaged and the power of the driving force source is transmitted through the second path, control the at least one of the input pulley hydraulic pressure or the output pulley hydraulic pressure larger than the clutch hydraulic pressure such that a winding radius of the belt on the at least one of the input-side pulley or the output-side pulley, to which a hydraulic pressure larger than the clutch hydraulic pressure is applied, decreases, and ii) when the clutch hydraulic pressure is larger than any of the input pulley hydraulic pressure (Pin) and the output pulley hydraulic pressure (Pout), control the input pulley hydraulic pressure and the output pulley hydraulic pressure such that a winding radius of the belt on the input-side pulley decreases and a winding radius of the belt on the output-side pulley increases.