Multi-Bernoulli mixture (MBM) filter is one of the exact closed-form multi-target Bayes filters in the random finite sets (RFS) framework, which utilizes multi-Bernoulli mixture density as the multi-target conjugate prior. This filter is the variant of Poisson multi-Bernoulli mixture filter when the birth process is changed to a multi-Bernoulli RFS or a multi-Bernoulli mixture RFS from a Poisson RFS. On the other hand, labeled multi-Bernoulli mixture filter evolves to MBM filter when the label is discarded. In this letter, we provide a complete derivation of MBM filter where the derivation of update step does not use the probability generating functional. We also describe the sequential Monte Carlo implementation and adopt Gibbs sampling for truncating the MBM filtering density. Numerical simulation with a nonlinear measurement model shows that MBM filter outperforms the classical probability hypothesis density filter.