A control device for fuel injection of an internal combustion engine, the internal combustion engine that is subject to control performed by the control device including a port injection valve that is arranged in use to inject fuel into an intake passage, wherein the control device is configured to execute: a requested injection amount calculation process (M30, M118, M32, M122) for calculating a requested injection amount (Qd) for controlling an air-fuel ratio to a target air-fuel ratio based on an air amount (NE, Ga) filling a cylinder of the internal combustion engine; and an operation process for operating the port injection valve in order to inject fuel of the requested injection amount (Qd), and the operation process includes a multiple injection process (S50: YES, S66) for injecting fuel in sequence from an intake asynchronous injection to an intake synchronous injection by splitting (S52 to S54) the fuel of the requested injection amount (Qd) so as to variably set a synchronous injection amount (Qs) and an asynchronous injection amount (Qns) in accordance with load (Qd) that is a physical quantity having a correlation with the filling air amount (NE, Ga) or in accordance with two parameters that are the load (Qd) and a temperature of the internal combustion engine, the synchronous injection amount (Qs) being an injection amount of the intake synchronous injection of injecting fuel in synchronization with an open period of an intake valve, the asynchronous injection amount (Qns) being an injection amount of the intake asynchronous injection of injecting fuel at a timing that is more advanced than a timing of the intake synchronous injection, wherein the operation process executes the multiple injection process on the condition that the temperature of the internal combustion engine is less than or equal to a predetermined temperature (S46: YES) and injects the fuel of the requested injection amount (Qd) with a single fuel injection when the temperature of the internal combustion engine is greater than the predetermined temperature (S46: NO), and the single fuel injection starts injecting at a timing that is more advanced than an open timing of the intake valve. a requested injection amount calculation process (M30, M118, M32, M122) for calculating a requested injection amount (Qd) for controlling an air-fuel ratio to a target air-fuel ratio based on an air amount (NE, Ga) filling a cylinder of the internal combustion engine; and an operation process for operating the port injection valve in order to inject fuel of the requested injection amount (Qd), and the operation process includes a multiple injection process (S50: YES, S66) for injecting fuel in sequence from an intake asynchronous injection to an intake synchronous injection by splitting (S52 to S54) the fuel of the requested injection amount (Qd) so as to variably set a synchronous injection amount (Qs) and an asynchronous injection amount (Qns) in accordance with load (Qd) that is a physical quantity having a correlation with the filling air amount (NE, Ga) or in accordance with two parameters that are the load (Qd) and a temperature of the internal combustion engine, the synchronous injection amount (Qs) being an injection amount of the intake synchronous injection of injecting fuel in synchronization with an open period of an intake valve, the asynchronous injection amount (Qns) being an injection amount of the intake asynchronous injection of injecting fuel at a timing that is more advanced than a timing of the intake synchronous injection, wherein the operation process executes the multiple injection process on the condition that the temperature of the internal combustion engine is less than or equal to a predetermined temperature (S46: YES) and injects the fuel of the requested injection amount (Qd) with a single fuel injection when the temperature of the internal combustion engine is greater than the predetermined temperature (S46: NO), and the single fuel injection starts injecting at a timing that is more advanced than an open timing of the intake valve.