An engine exhaust purification device comprising: a filter that is arranged in an exhaust pipe of an engine and traps fine particles that are suspended in an exhaust passing through the exhaust pipe; a burner including a fuel injection nozzle and arranged at a position located at an upstream side of the filter in the exhaust pipe, wherein the burner burns fuel injected from the fuel injection nozzle and heats the exhaust to increase the temperature of the filter and remove the fine particles trapped in the filter; and a control unit that controls a fuel injection mode of the fuel injection nozzle, characterized in that a period including a single fuel injection period and a single injection stop period is set as a single injection cycle, the fuel injection period is a period in which fuel is injected for a number of times at a predetermined frequency, the injection stop period is a variable period in which the injection of fuel is stopped, the control unit controls the fuel injection nozzle so that the fuel injection nozzle injects fuel in accordance with the injection cycle, the control unit is configured to lengthen the injection stop period as the temperature of the filter increases, the fuel injection period is a first fuel injection period, a period of one of a number of injections repeated at the predetermined frequency in the first fuel injection period is a second fuel injection period (Ton), the engine includes an intake pipe that supplies air to the burner, the control unit is configured to lengthen the second fuel injection period (Ton) as the air amount supplied to the burner increases in the first fuel injection period, and the control unit is configured to set the second fuel injection period (Ton) so that a ratio of a total amount of fuel injected in the first fuel injection period and an air amount supplied to the burner in the first fuel injection period conforms to the stoichiometric air-fuel ratio. a filter that is arranged in an exhaust pipe of an engine and traps fine particles that are suspended in an exhaust passing through the exhaust pipe; a burner including a fuel injection nozzle and arranged at a position located at an upstream side of the filter in the exhaust pipe, wherein the burner burns fuel injected from the fuel injection nozzle and heats the exhaust to increase the temperature of the filter and remove the fine particles trapped in the filter; and a control unit that controls a fuel injection mode of the fuel injection nozzle, a period including a single fuel injection period and a single injection stop period is set as a single injection cycle, the fuel injection period is a period in which fuel is injected for a number of times at a predetermined frequency, the injection stop period is a variable period in which the injection of fuel is stopped, the control unit controls the fuel injection nozzle so that the fuel injection nozzle injects fuel in accordance with the injection cycle, the control unit is configured to lengthen the injection stop period as the temperature of the filter increases, the fuel injection period is a first fuel injection period, a period of one of a number of injections repeated at the predetermined frequency in the first fuel injection period is a second fuel injection period (Ton), the engine includes an intake pipe that supplies air to the burner, the control unit is configured to lengthen the second fuel injection period (Ton) as the air amount supplied to the burner increases in the first fuel injection period, and the control unit is configured to set the second fuel injection period (Ton) so that a ratio of a total amount of fuel injected in the first fuel injection period and an air amount supplied to the burner in the first fuel injection period conforms to the stoichiometric air-fuel ratio.