Variational Quantum Algorithms (VQAs) hold promise for near-term quantum computing applications, but their high measurement demands pose a significant challenge. This work addresses this challenge by introducing a novel recursive estimation algorithm for VQAs. Our approach leverages advanced estimation techniques to markedly reduce the total number of shots required for VQA optimization. We provide theoretical bounds for the bias and variance of our estimator and demonstrate its effectiveness in reducing the shot count while maintaining accuracy. This advancement paves the way for more efficient and practical implementation of VQAs on current quantum hardware.