Abstract Star formation can produce bubbles and outflows, as a result of stellar feedback. Outflows and bubbles inject momentum and energy into the surrounding interstellar medium, and so are related to the overall energy balance of the molecular cloud. Molecular bubbles can be resolved by higher-resolution radio telescopes to quantify the effect of star formation on molecular clouds. We report here the identification of a new molecular bubble with an outflow, and a Herbig–Haro object, HH 319, located at the bubble center. Multiwavelength data have been utilized to study its spatial structure, energy injection, and dynamical timescale. This bubble has a kinetic energy of 5.8 × 10 43 erg within the smallest radius of a bubble in Taurus, 0.077 pc. The bubble formed ∼70,000 yr ago. According to the proper-motion velocities of protostars from Gaia EDR3, the T Tauri binary stars (FY Tau and FZ Tau) at the southwest edge of the bubble may have produced the outflow–bubble structure. This is an unusual new structure found in low- and intermediate-mass star formation regions. Only a bubble in Orion A, driven by V380 Ori, has a similar structure. The bubble–outflow structure provides additional observational evidence for the theory of stellar wind from T Tauri stars. It enhances our understanding of how stellar feedback acts on molecular clouds.