In this paper, a recursive subspace identification method is proposed to identify linear time-invariant systems subject to load disturbance with relatively slow dynamics. Using the linear superposition principle, the load disturbance response is decomposed from the deterministic-stochastic system response in the form of a time-varying parameter. To ensure unbiased estimation of the deterministic system matrices, a recursive least-squares (RLS) identification algorithm is established with a fixed forgetting factor, while another RLS algorithm with an adaptive forgetting factor is constructed based on the output prediction error to quickly track the time-varying parameter of load disturbance response. By introducing a deadbeat observer to represent the deterministic system response, two extended observer Markov parameter matrices are constructed for recursive estimation. Consequently, the deterministic matrices are retrieved from the identified system Markov parameter matrices. The convergence of the proposed method is analysed with a proof. Two illustrative examples are shown to demonstrate the effectiveness and merit of the proposed identification method.