It is essential to control concentration gradients at specific locations for many biochemical experiments. This paper proposes a tunable concentration gradient generator actuated by acoustically oscillating bubbles trapped in the bubble channels using a controllable position based on the gas permeability of polydimethylsiloxane (PDMS). The gradient generator consists of a glass substrate, a PDMS chip, and a piezoelectric transducer. When the trapped bubbles are activated by acoustic waves, the solution near the gas–liquid interface is mixed. The volume of the bubbles and the position of the gas–liquid interface are regulated through the permeability of the PDMS wall. The tunable concentration gradient can be realized by changing the numbers and positions of the bubbles that enable the mixing of fluids in the main channel, and the amplitude of the applied voltage. This new device is easy to fabricate, responsive, and biocompatible, and therefore has great application prospects. In particular, it is suitable for biological research with high requirements for temporal controllability.