  In this paper, we make an attempt to combine the neutrino trimaximal (TM1 and
TM2) mixings and $\mu$-$\tau$ reflection symmetry in the type-I seesaw model.
Such a scenario is highly restrictive and predictive: in addition to three
right-handed neutrino masses, there are only five real parameters; all the
lepton flavor mixing parameters except for $\theta^{}_{13}$ will be predicted.
The relations between the model parameters and the measurable neutrino
parameters will be derived. The implications of this scenario for leptogenesis
will be explored in detail. A further reduction of this scenario to the more
restrictive and predictive minimal seesaw model with only two right-handed
neutrinos will also be considered. In addition, we will also discuss a possible
approach to get the desired mass matrices and study the compatibility of the
trimaximal $\mu$-$\tau$ reflection symmetry with texture zeros.
