The present invention relates to a steam supply system and method for a ship capable of economically generating and supplying steam in accordance with the demand for steam on board while suppressing the operation of an auxiliary boiler that generates steam using fuel. The steam supply system for a ship according to the present invention comprises: an economizer for producing steam by recovering waste heat from exhaust gas of an engine; SCR device for denitrifying the exhaust gas of the engine; A burner generating reaction heat required for the denitrification reaction; A first flue gas valve for controlling a flow path so that flue gas is supplied from the burner to the SCR device; A second flue gas valve for controlling a flow path so that flue gas is supplied from the burner to the economizer; And a control unit that controls whether or not the burner is operated according to the steam production amount of the economizer, allocates a load of the burner, and controls the second flue gas valve regardless of whether the SCR device is operated or not, wherein the control unit comprises: , It characterized in that the flue gas is supplied from the burner to one or more of the SCR device and the economizer.
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