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This paper presents a least-mean-square (LMS) algorithm for the joint estimation of acoustic and mean flow velocities from laser Doppler velocimetry (LDV) measurements. The usual algorithms used for measuring with LDV purely acoustic velocity or mean flow velocity may not be used when the acoustic field is disturbed by a mean flow component. The LMS-based algorithm allows accurate estimations of both acoustic and mean flow velocities. The Cramer-Rao bound (CRB) of the associated problem is determined. The variance of the estimators of both acoustic and mean flow velocities is also given. Simulation results of this algorithm are compared with the CRB, and the comparison leads us to validate this estimator.