Microtubules establish the directionality of intracellular transport by kinesins and dynein through their polarized assembly, but it remains unclear how directed transport occurs along microtubules organized with mixed polarity. We investigated the ability of the plus-end directed kinesin-4 motor KIF21B to navigate mixed polarity microtubules in mammalian dendrites. Reconstitution assays with recombinant KIF21B and engineered microtubule bundles or extracted neuronal cytoskeletons indicate that nucleotide-independent microtubule binding regions of KIF21B modulate microtubule dynamics and promote directional switching on antiparallel microtubules. Optogenetic recruitment of KIF21B to organelles in live neurons resulted in unidirectional transport in axons but bi-directional transport with a net retrograde bias in dendrites; microtubule dynamics and the secondary microtubule binding regions are required for this net directional bias. We propose a model in which cargo-bound KIF21B motors coordinate nucleotide-sensitive and insensitive microtubule binding sites to achieve net retrograde movement along the dynamic mixed polarity microtubule arrays of dendrites.