Abstract: A new method of Error-calibrated and Attributed Relational Matchina Neural Network (EARGMNN) has been developed in this paper. Attributed Relational Graphs (ARG), there are direction arcs and multi-arcs. So ARG is asymmetric, but the Hopfield Net is symmetry. After redefining the distances of node feature and node-relational arc feature, we solved these asymmetry problem. At the same time, the idea of error-calibration has been introduced into neural network. Then the net can be used as random semantic net matching. The analogue annealing method has been introduced in EARGMNN model also, the test results are quite satisfactory.