The special starts with Woodstock following holes dug by Linus, who is looking for his security blanket. In the next scene, Charlie Brown is shown playing baseball with his friends, where Linus is criticized for bringing his blanket. Later, Lucy informs Linus that their grandmother is coming this weekend, and if Linus doesn't get rid of his blanket, it will be cut up into pieces by their grandmother. Meanwhile, Schroeder is playing piano, and Lucy tries to get him to notice her, with her only obstacle being a bust on Schroeder's piano. Charlie Brown suggests that Linus finds a substitute, which only worked to some extent. In the meantime, Violet and Patty roast Pig-Pen for his dirt cloud. Later, Lucy decides to lock Linus' blanket in the closet for the day, and this time, Linus is to have no substitutes for his blanket. The next day, Snoopy steals Linus' blanket again, and Lucy turns it into a kite, which gets lost after she lets go of it. Later, Lucy smashes the bust on Schroeder's piano, only for him to have a replacement bust. A few days later, Linus gets his blanket back, only for Lucy to bury it, which leads to the scene the special started at. Snoopy digs up the blanket for Linus, probably out of pity. The next day, Snoopy drags Linus and his blanket across the neighborhood, which all the children follow as they get affected in their path. After all the children criticize Linus to his limit, he finally delivers a monologue about how everyone needs some security, while pointing out their own securities that are like his blanket (Sally's being "Sweet Baboo"s, Schroeder's being Beethoven, and Snoopy's being suppertime, “24 hours a day”). Later, Grandma Van Pelt arrives, and Linus gives her a wash cloth as a decoy of his blanket. The story ends with Linus trying to get his blanket back after Snoopy steals it, shouting "AUGH!!"