In this article, a differential game of evasion is explored for the linear motion dynamics of players (Pursuer and Evader) when the Pursuer control is subject to geometric constraint (or 𝐺-constraint) and the Evader control is subject to Grönwall-type constraint (or 𝐺𝑟-constraint). To solve the evasion problem, we propose a particular strategy for evader and study its structure depending on the parameters.