Background: Survival extrapolation is essential in the cost-effectiveness analysis to quantify the lifetime survival benefit associated with a new intervention, due to the restricted duration of randomized controlled trials (RCTs). Current approaches of extrapolation often assume that the treatment effect observed in the trial can continue indefinitely, which is unrealistic and may have a huge impact on decisions for resource allocation. Objective: We introduce a novel methodology as a possible solution to alleviate the problem of performing survival extrapolation with heavily censored data from clinical trials. Method: The main idea is to mix a flexible model (e.g., Cox semi-parametric) to fit as well as possible the observed data and a parametric model encoding assumptions on the expected behaviour of underlying long-term survival. The two are ‘blended’ into a single survival curve that is identical with the Cox model over the range of observed times and gradually approaching the parametric model over the extrapolation period based on a weight function. The weight function regulates the way two survival curves are blended, determining how the internal and external sources contribute to the estimated survival over time. Results: A 4-year follow-up RCT of rituximab in combination with fludarabine and cyclophosphamide v. fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia is used to illustrate the method. Conclusion Long-term extrapolation from immature trial data may lead to significantly different estimates with various modelling assumptions. The blending approach provides sufficient flexibility, allowing a wide range of plausible scenarios to be considered as well as the inclusion of genuine external information, based e.g. on hard data or expert opinion. Both internal and external validity can be carefully examined.