We propose a modified quantum teleportation scheme to increase the teleportation accuracy by applying a cubic phase gate to the displaced squeezed state. We describe the proposed scheme in the Heisenberg picture, evaluating it from the point of view of adding an error in teleportation, and show that it allows achieving less error than the original scheme. Repeating the description in the Schrödinger picture, we find the range of the displacement values at which our conclusions are valid. Using the example of teleportation of the vacuum state and the squeezed states, we show that the scheme allows one to achieve high-fidelity values.