The story begins much like the classic fairy tale, with Red Riding Hood off to see her grandmother, who lives in the woods. The present she plans to bring her grandmother is Tweety (in his cage). Sylvester sees Red's cargo and immediately begins going after her, his primary interest being Tweety. Red boards the bus, but Sylvester continues after her as it drives into the woods, the inattentive cat striking a road sign along the way.
In the woods, the Big Bad Wolf — rougher looking in appearance than in later shorts — waits for Red to come by. A sign announces who Big Bad is, much to his disgust. Sylvester overhears the requisite exchange of Big Bad asking Red where she is headed and soon joins Big Bad in trying to reach Granny's house first.
Big Bad ousts Granny from the house, to which she immediately swears revenge (mimicking Ralph Kramden's signature lines). Big Bad and Sylvester hurriedly dress in Granny's clothing in anticipation of Red's arrival. Big Bad takes his place in the bed after shooing Sylvester underneath. Once Red arrives and presents "Grandma" with Tweety, she sets it down as asked; Sylvester immediately approaches the cage, prompting Tweety to ask: "Hewwo, Wittle Wed Widing Hood's Gwandma! Whatcha doin' under da bed?" After the signature exchange ending with "The better to see, smell, and eat you with," and each character's realization of their sworn enemy (Red: "Oh! The Big Bad Wolf!" Tweety: "Eek! The Big Bad Puddy Tat!"), the chase begins.
After several back-and-forth chases, with Big Bad and Sylvester getting the worse end of things, Red and Tweety flee Granny's home and head for the nearest bus stop. Their pursuers chase after the bus and immediately board at the next stop, only to be forcibly ejected by none other than Granny, who then shouts, "I told them, one of these days...!" Red and Tweety supply the rest of the line: "Pow! Right/wight in the kisser!" The screen irises out.