The present invention provides an evaporative fuel processing device. In an evaporative fuel processing device having a stepping motor type closure valve in a vapor passage connecting a canister to afuel tank, it is possible to appropriately control the gas flow through the closure valve when performing a pressure reduction operation of the fuel tank. An evaporative fuel treating apparatus includes: a canister; a vapor passage configured to cause a fuel tank to communicate with the canister; a closure valve including a valve disc arranged in the vapor passage and a stepping motor configured to open and close the valve disc; and a control device configured to control the closure valve. The control device is configured, in opening the valve disc to perform a pressure relief operation of thefuel tank, to: execute a flow rate estimation processing that calculates an estimated flow rate of gas passing through the closure valve, based on the absolute value of the amount of change of in-tank pressure of the fuel tank and a space volume inside the fuel tank; and execute a motor control processing that controls the number of steps of the stepping motor such that the estimated flow rate approaches a required flow rate.