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This paper is concerned with the filter design for Markov jump systems with incomplete transition probabilities subject to sensor nonlinearities. Moreover, the frequency of disturbance ranges in a finite interval. To set up a solvable solution to cast the filter parameters, nonlinearities induced by unknown transition probabilities are coped with the transition probability property and the S-procedure is adopted to handle sensor nonlinearities. With these strategies, sufficient conditions for the filtering error systems to be stochastically stable with the required finite frequency performance are established firstly. Then, a finite frequency filter design method is proposed in terms of linear matrix inequalities. The proposed finite frequency filter method covers the full frequency as a special case. Its effectiveness is verified by a numerical example.