Conventionally, job processing times are assumed to be constant from the first job to be processed until the last job to be completed. However, recent empirical studies in several industries have verified that unit costs decline as firms produce more of a product and gain knowledge or experience. This phenomenon is known as the "learning effect." In this paper a bicriteria m-identical parallel machine scheduling problem with a learning effect is considered. The objective function of the problem is to find a sequence that minimizes a weighted sum of total completion time and total tardiness. Total completion time and total tardiness are widely used performance measures in scheduling literature. To solve this scheduling problem, a mathematical programming model is formulated.