This paper proposes a new approach for the estimation of unknown and time-varying specific growth rate in fed-batch bioprocess. A novel adaptive estimation technique based on the concept of invariant manifold is proposed as an effective approach to estimate growth kinetic parameters. An asymptotic nonlinear observer is used to provide simultaneous on-line estimation of biomass concentration and growth kinetic. The method is easy to implement and requires only one tuning parameter. The effectiveness of the proposed algorithm is illustrated with representative bioreactor simulation examples. (C) 2014 Elsevier Ltd. All rights reserved.