We introduce a new class of "filtered" schemes for some first order nonlinear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013). The proposed schemes are not monotone but still satisfy some ϵ-monotone property. Convergence results and precise error estimates are given, of order 1/2 with respect to the mesh size. The framework allows to construct finite difference discretizations that are easy to implement, high order where the solution is smooth, and provably convergent, together with error estimates. Numerical tests on several examples are given to validate the approach, also showing how the filtered approach can stabilize an otherwise unstable high-order scheme.