A controller for an internal combustion engine, the internal combustion engine comprising a port injection valve that injects fuel into an intake passage, the controller being configured to execute: a base injection amount calculation process for calculating a base injection amount (Qb) in accordance with an amount of fresh air filling a combustion chamber of the internal combustion engine; an increasing correction process for increasing the base injection amount (Qb) over a predetermined period after the internal combustion engine is started by setting the initial value of a collection amount increase ratio (efase1) of the base injection amount (Qb) and gradually decreasing the collection amount increase ratio (efase1) of the base injection amount (Qb) over the predetermined period; and a fuel injection process for selecting and executing one of two processes, a multiple injection process and a single injection process, in order to inject the increased base injection amount (Qd) of fuel, wherein the multiple injection process is to sequentially execute an intake air synchronous injection and an intake air non-synchronous injection by operating the port injection valve in order from the intake air non-synchronous injection to the intake air synchronous injection, the single injection process is to inject the increased base injection amount (Qd) of fuel by operating the port injection valve through the intake air non-synchronous injection, the intake air synchronous injection is to inject fuel in synchronization with an opening period of an intake valve, and the intake air non-synchronous injection is to inject fuel at a more advanced timing (Ins) than a timing of the intake air synchronous injection, wherein the increasing correction process includes a differentiation process for setting the collection amount increase ratio (efase1) to be a smaller value (Km < 1) in the multiple injection process than in the single injection process. a base injection amount calculation process for calculating a base injection amount (Qb) in accordance with an amount of fresh air filling a combustion chamber of the internal combustion engine; an increasing correction process for increasing the base injection amount (Qb) over a predetermined period after the internal combustion engine is started by setting the initial value of a collection amount increase ratio (efase1) of the base injection amount (Qb) and gradually decreasing the collection amount increase ratio (efase1) of the base injection amount (Qb) over the predetermined period; and a fuel injection process for selecting and executing one of two processes, a multiple injection process and a single injection process, in order to inject the increased base injection amount (Qd) of fuel, wherein the multiple injection process is to sequentially execute an intake air synchronous injection and an intake air non-synchronous injection by operating the port injection valve in order from the intake air non-synchronous injection to the intake air synchronous injection, the single injection process is to inject the increased base injection amount (Qd) of fuel by operating the port injection valve through the intake air non-synchronous injection, the intake air synchronous injection is to inject fuel in synchronization with an opening period of an intake valve, and the intake air non-synchronous injection is to inject fuel at a more advanced timing (Ins) than a timing of the intake air synchronous injection, the multiple injection process is to sequentially execute an intake air synchronous injection and an intake air non-synchronous injection by operating the port injection valve in order from the intake air non-synchronous injection to the intake air synchronous injection, the single injection process is to inject the increased base injection amount (Qd) of fuel by operating the port injection valve through the intake air non-synchronous injection, the intake air synchronous injection is to inject fuel in synchronization with an opening period of an intake valve, and the intake air non-synchronous injection is to inject fuel at a more advanced timing (Ins) than a timing of the intake air synchronous injection, wherein the increasing correction process includes a differentiation process for setting the collection amount increase ratio (efase1) to be a smaller value (Km < 1) in the multiple injection process than in the single injection process.