For the Haldane phase, the magnetic field usually tends to drive the system into a topologically trivial phase. Here we report a novel reentrance of the Haldane phase at zero temperature in the spin-1 antiferromagnetic Heisenberg model on a sawtooth chain. A partial Haldane phase is induced by the magnetic field, which is the combination of the Haldane state in one sublattice and a ferromagnetically ordered state in the other sublattice. Such a partial Haldane phase should be protected by the bond centered inversion symmetry, and is a result of the zero-temperature entropy due to quantum fluctuations and geometrical frustration.