The invention provides a fluid heater in which the efficiency of heat transfer to a fluid is improved, downsizing of the heater itself can be achieved, and the rise time until warm water heated to a necessary temperature is supplied is shortened, which results in reduction of the power consumption. The heater includes a flat ceramic substrate (1) and a beating element formed on one surface of or in the interior of the ceramic substrate (1). The ceramic substrate (1) is made of AlN, etc. or silicon nitride, whose thermal conductivity is 50 W/m·K or more. A zigzag water channel is formed by walls 6, etc., on the fluid-heating surface of the ceramic substrate (1). A plurality of fins 5 are fixed in the water channel. A heat insulating material 8 can be mounted so as to cover a surface excluding the fluid-heating surface of the ceramic substrate (1).