We report on the first experimental observation, to the best of our knowledge, of soliton molecules in a spatiotemporal mode-locked multimode fiber (MMF) laser. By adjusting the waveplates inside the cavity, not only the spatiotemporal mode-locking state with a stable single pulse but also soliton molecules are observed. Various soliton molecules, including soliton pairs, soliton triplets, and soliton quartets with different pulse separations, are achieved. Transition of different operation states with pump power is given. The results would be beneficial for further understanding of the nonlinear dynamics in spatiotemporal mode-locked MMF lasers.