Good-quality and fine-grain Bi6Fe2Ti3O18 magnetic ferroelectric films with single-phase layered perovskite structure have been prepared successfully via the metal organic decomposition (MOD) method. The results of low-temperature magnetocapacitance measurements reveal that an ultra-low magnetic field of 10 Oe can produce a non-trivial magnetodielectric response in zero-field cooling conditions, and the relative variation of dielectric constants in a magnetic field is positive, i.e. [ epsilon(r)(H) - epsilon(r)(0)]/epsilon(r)(0) = 0.05, when T < 55 K, but negative with a maximum of [ epsilon(r)(H) - epsilon(r)(0)]/epsilon(r)(0) = - 0.14 when 55 K < T < 190 K. The magnetodielectric effect shows a sign change at 55 K, which is due to a transition from an antiferromagnetic to a weak ferromagnetic, and vanishes abruptly at around 190 K, which is thought to be associated with an order - disorder transition of iron ions at the B site of perovskite structures. Our results allow the expectation of low-cost applications of detectors and switches for extremely weak magnetic fields over a wide temperature range of 55 - 190 K.