Measuring the ultrasound velocity change ΔV s V s as a function of temperature T in BaPb 1− x Bi x O 3 (x = 0.4), we have found a remarkably large jump and hysteresis in ΔV s V s versus T. This first order phase transition accompanies a prominent critical slowing down phenomenon against the time after fixing T in the cooling process. Scaling the time appropriately, all curves with different time dependences can be folded into only one curve, following the scaling law in the first order phase transition. An X-ray diffraction analysis shows that this first order phase transition is associated with a structural phase transition from the orthorhombic structure to the monoclinic one.