The performance of units in the same batch can exhibit considerable heterogeneity due to the variation in the raw materials and fluctuation in the manufacturing process. For products suffering performance degradation in their use, such heterogeneity often results in an increase in the dispersion of the degradation paths of units in a population. The degradation rate of products can be unit-specific and often treated as random effects. This paper develops a novel random-effects Wiener process model to account for the unit-to-unit heterogeneity in the degradation, where the generalized inverse Gaussian (GIG) distribution is used to model the unit-specific degradation rate. The GIG distribution is a very general distribution with broad applications, which includes the inverse Gaussian (IG) distribution and the Gamma distribution as special cases. We investigate the model properties and develop an expectation maximization (EM) algorithm for parameter estimation. By comparing the proposed model with existing models on two real degradation datasets of the infrared LEDs and the GaAs lasers, we show that the proposed model is quite effective for degradation modeling with heterogeneous rates.