This article introduces the almost unbiased gamma ridge regression estimator (AUGRRE) estimator based on the gamma ridge regression estimator (GRRE). Furthermore, some shrinkage parameters are proposed for the AUGRRE. The performance of the AUGRRE by using different shrinkage parameters is compared with the existing GRRE and maximum likelihood estimator. A Monte Carlo simulation is carried out to assess the performance of the estimators where the bias and mean squared error performance criteria are used. We also used a real-life dataset to demonstrate the benefit of the proposed estimators. The simulation and real-life example results show the superiority of AUGRRE over the GRRE and the maximum likelihood estimator for the gamma regression model with collinear explanatory variables.