Let Y be a smooth projective 3-fold admitting a K3 fibration f: Y  -> P1 with -K_{Y} = f^*O(1). We show that the pseudo-automorphism group of Y acts with finitely many orbits on the codimension one faces of the movable cone if H^{3}(Y, C) = 0, confirming a special case of the Kawamata-Morrison-Totaro cone conjecture. In Coates-Corti-Galkin-Kasprzyk 2016, Przyjalkowski 2018, and Cheltsov-Przyjalkowski 2018, the authors construct log Calabi-Yau 3-folds with K3 fibrations satisfying the hypotheses of our theorem as the mirrors of Fano 3-folds.