<p>The McKean-Vlasov filtering problem is a special kind of filtering problem, with the state and/or observation processes governed by McKean-Vlasov stochastic differential equations, which has extensive applications in various scenarios. In this paper, the authors will propose a novel numerical algorithm to solve the McKean-Vlasov filtering problem based on the Hermite spectral method under the framework of Yau-Yau algorithm. As the first approach to numerically solving the Duncan-Mortensen-Zakai equation associated with the McKean-Vlasov filtering problem, the proposed algorithm can provide accurate estimations of the conditional expectation and conditional probability density of the state process with a reasonable online computational complexity. The efficiency of the proposed algorithm is verified both theoretically and numerically in this paper.</p>