In this paper, a linear unbiased minimum-variance filtering problem is considered for a class of systems with randomly multi-step sensor delays. A new mathematical model is established for the multi-step sensor delays. Different from the augmented method for dealing with delayed systems, a linear unbiased minimum-variance filter design method is proposed without augmenting the state vector, which effectively reduces the filter dimensions. A recursive algorithm for calculating the filter gain matrix is developed. The simulation results illustrate the effectiveness of the proposed method.