We have investigated the structural, dynamical, and topological phase in the ternary chalcogenide material SnPbSe2 using first-principles calculations. This material is theoretically optimized in the rhombohedral crystal structure system. The dynamical stability analysis shows that this material is dynamically unstable at ambient conditions but becomes stable under 2% of applied uniaxial and biaxial strain. At ambient conditions, this material shows no band inversion in the bulk band structure and becomes a topologically trivial semiconductor. But, under the effect of 2% biaxial strain along equal lattice parameters, the spin–orbit coupling (SOC) is enhanced and a band inversion appeared at time-reversal invariant momenta (TRIM) F-point. Further increase in biaxial strain shows another band inversion at the Γ-point, which makes this material topologically trivial again. We have calculated the Z2 topological invariants with the help of the product of parities at the TRIM points, which further confirms the topological phase transition in SnPbSe2.