An orthogonal matching pursuit iterative identification algorithm is proposed for dual-rate sampled output-error systems with unknown time-delays and orders based on finite number of sampled data. Firstly, the identification model of the target system is established based on the dual-rate sampled data. Secondly, considering the input time-delay and the system order are both unknown, by means of the overparameterization method and taking the regression items of the noise-free output data and that of the input data as sufficient length, a sparse system is derived and its sparsity is the number of parameters to be identified. Furthermore, the idea of auxiliary model and the sparse recovery method in compressed sensing are combined for interactive estimation of the parameter vector and the noise-free outputs, where the parameter vector is estimated by using the orthogonal matching pursuit algorithm, the auxiliary model is constructed based on which and then the noise-free outputs are calculated accordingly and applied in turn for updating the parameter vector. Finally, the system order and the input time-delay are calculated according to the structure of the obtained parameter vector. The simulation experiments verify that the proposed algorithm can provide accurate joint estimation of system parameters, time-delay and order based on small amounts of sampled data.