The magnetodielectric (MD) effect for BiMn7O12 with the cubic A′A″3B4O12-type A-site-ordered perovskite structure has been investigated. A clear negative MD response around and beyond TN has been observed and attributed to antiferromagnetic spin fluctuations. With further decreasing temperature (T⪡TN) a switching to a complex positive MD effect is found confirming additional contribution coming from the magnetic ordering. The present study underlines the importance of square-coordinated MnA″O2 units for generating MD coupling in an A′A″3B4O12-type structure; the magnitude of the MD effect then strongly depends on the precise chemical composition.