When amplitude of the vibrating pendulum is small then θ is small.
Here the restoring force F = -mg sin θ = -mgθ = -mgx/l,
where x is the displacement of bob and l is the length of pendulum.
Hence F ∝ -x. Since F is directed towards mean position.
Therefore, the motion of the bob of simple pendulum will be SHM, if θ is small.