The planar Ramsey number PR (H₁, H₂) is the smallest integer n such that any planar graph on n vertices contains a copy of H₁ or its complement contains a copy of H₂. It is known that the Ramsey number R(K₄ -e, K₆) = 21, and the planar Ramsey numbers PR(K₄ - e, K_l) for l ≤ 5 are known. In this paper, we give the lower bounds on PR (K₄ ? e, K_l) and determine the exact value of PR (K₄ - e, K₆).