In this paper, a recursive algorithm for blackbox identification of linear parameter-varying (LPV) systems is proposed. The algorithm belongs to the class of subspace identification methods and is based on an existing LPV subspace identification algorithm with block-processing, which is modified and extended to the recursive estimation scenario. These modifications are related to existing methods of recursive subspace identification for linear and time-invariant (LTI) systems, but offer additional room for improvement of the identification results in the LPV case. Therefore, an extension of the recursive algorithm is introduced that avoids the simplifying assumption of one dominating local linear model in the LPV system, which is made in the block-processing algorithm. It is shown that with this extension the recursive algorithm can lead to even better identification results than the corresponding algorithm with block-processing.