In this work, we studied Lie symmetry and the conservation law of the conformable fractional Burgers' equation. We discussed the physical significance of the conformable Burgers' equation, as well as the behavior of the fluid that satisfies this equation. As an application, we calculated the group invariant solutions corresponding to an optimal system of one-dimensional subalgebras of the Lie algebra of infinitesimal point symmetries of this equation under the condition that the three spatial derivative orders of the equation are consistent.