The dielectric properties of single-crystal CH3NH3AlBr4 have been studied. The crystal belongs to the tetragonal system at room temperature. It shows ferroelectricity along the a-direction below the Curie temperature Te = 76.6 K. The dielectric constant along the a-direction obeys a Curie Weiss law above T-c with the Curie constant being 3.7 x 10(2) K. The spontaneous polarization measured by means of 50 Hz hysteresis loop at 64 K is 6.6 x 10(-3) C/m(2). Besides the ferroelectric transition, a first order structural phase transition is found at about 250 K.