[en] This paper presents a new method for two-dimensional image reconstruction by using a multi-layer neural network. Though a conventionally used object function of such a neural network is composed of a sum of squared errors of the output data, we define an object function composed of a sum of squared residuals of an integral equation. By employing an appropriate numerical line integral for this integral equation, we can construct a neural network which can be used for CT image reconstruction for cases with small amount of projection data. We applied this method to some model problems and obtained satisfactory results. This method is especially useful for analyses of laboratory experiments or field observations where only a small amount of projection data is available in comparison with the well-developed medical applications