This paper presents a Hopfield neural network approach for the problem of scheduling n jobs in a single machine to minimize total weighted tardiness. A binary encoding scheme is introduced to represent the solutions, together with a heuristic to decode. A 10-job problem is solved by sequencing the job using different methods viz. weighted shortest processing time (WSPT) rule, Earliest Due Date (EDD) rule, binary representation and Hopfield Neural Network. The results show that the Hopfield neural network performs better over others.