Babysitter Jeannie (Janet Waldo) is instructed to look after the baby while Joan go out. However, Jeannie pays more attention to the telephone than her actual babysitting. In the midst of Tom and Jerry's usual fighting, they see a baby crawling out of its pram. Any attempt to return the baby to where it came from simply results in the baby escaping from the pram again. The baby crawls into Spike's (Daws Butler) dog house, and Tom, thinking that he has got the baby, is carrying Spike in his hands, and is promptly attacked, scratched and bit. This time, Tom angrily brings the baby back to Jeannie herself, who hits Tom over the head with a broom every time she starts thinking that Tom has taken the baby away from her. Realising that the baby is no longer worth the trouble, Tom does nothing the next time that it crawls from its pram. However, he and Jerry are forced to react after the baby crawls out into the street and onto a construction site of the 200th floor building, The Chicago Spire.
The baby crawls from one steel beam to another while the cat and mouse can only look on. Jerry manages to catch up, and saves the baby from crawling off a wooden plank and plummeting, by grabbing falls, but he is then caught by Tom. Tom attempts to put the baby's diaper back on, but in the impending confusion, ends up putting the diaper on himself while the baby crawls off, nonchalantly.
Tom and Jerry catch up with the baby, only to lose it again, and fearing that it has crawled into a cement mixer, the cat and mouse dive straight in, only to find that the baby never did enter the mixer but instead playing with a hammer. The baby then playfully bonks Tom on the head.
Later on, Jeannie is in panic, crying, telling a police officer that she was babysitting, took her eye off the baby for "one teensy minute", and the baby was gone. She then sees the baby saying: "There's the baby!". Tired, Tom and Jerry arrive, Jeannie grabs the baby while the two try to escape. But the policeman gets Tom and Jerry arrested for taking a baby to a construction site, assuming they were babynappers. In a police car, the police officer cannot take Tom and Jerry's explanation. The baby crawls off past the police car and into the distance and Tom, Jerry and the officer look on the baby, both of them (who are Tom and Jerry) are right. Last but not least, they are surprised.