We report the magnetic and electric properties of Ba3NiNb2O9, which is a quasi-two-dimensional spin-one triangular-lattice antiferromagnet with trigonal structure. At low T and with increasing magnetic field, the system evolves from a 120 degree magnetic ordering phase (A phase) to an up-up-down (uud) phase (B phase) with a change of slope at 1/3 of the saturation magnetization, and then to an "oblique" phase (C phase). Accordingly, the ferroelectricity switches on at each phase boundary with appearance of spontaneous polarization. Therefore, Ba3NiNb2O9 is a unique triangular-lattice antiferromagnet exhibiting both uud phase and multiferroicity.