The Grudge

The Grudge describes a curse that is born when someone dies in the grip of a powerful rage or extreme sorrow. The curse is an entity created where the person died. Those who encounter this evil supernatural force die; and the curse is reborn repeatedly, passed from victim to victim in an endless, growing chain of horror. The following events are explained in their actual order; the original film is presented in a non-linear narrative.
The Saeki family lived happily in suburban Tokyo, but housewife Kayako Saeki fell in love with her college professor, Peter Kirk, obsessively writing about him in her diary. However, her husband Takeo discovered the diary. Believing Kayako was having an affair, he became mentally disturbed and murdered his wife by pushing her off the stairs, snapping her neck to a 90 degree angle and crushing her throat. He then drowned his young son Toshio - who witnessed the act - in the bathtub to cover his tracks, along with the pet cat, Mar. Takeo hid the bodies in the attic and closet, before Kayako's ghost murdered him by hanging him with her hair in Toshio's bedroom. Peter came to the Saeki house to speak to Kayako after receiving a letter from her, only to find her corpse. Shocked, he fled the house, killing himself the next day by falling over the balcony of his building complex in front of his wife. The Saeki family rose again as ghosts due to their rage and sorrow, notably Kayako, who appears as an onryÅ ghost, leaving the curse on the house.
The present timeline starts a few years later with the Williams family moving in from America. While husband Matt is thrilled with the house, his wife Jennifer and dementia-ridden mother Emma feel uncomfortable. Jennifer is quickly consumed by the curse. Matt returns home to find the house trashed, Emma upset, and his wife dying. Matt and Jennifer are killed by Toshio. Yoko, a careworker, arrives at the house the next day to find Emma alone, and encounters Kayako, who attacks her. Concerned about Yoko's disappearance, her employer Alex sends another careworker, Karen Davis, to take over the care for Emma. At the house, Karen is shocked when she finds a seemingly alive Toshio and Mar in the closet, contacting Alex for help.
Alex finds Emma dead in the house and Karen in a state of shock after her first encounter with Kayako, and summons the police, including Detective Nakagawa. Nakagawa and his partner Igarashi explore the house, finding the bodies of Matt and Jennifer in the attic along with a human's lower jaw. Matt's sister Susan disappears after being followed and attacked by Kayako, and Alex is killed when visited by a Kayako-possessed Yoko missing her lower jaw. Karen begins to be haunted by Kayako herself, informing her boyfriend Doug of the situation. She researches the origins of the house, eventually confronting Nakagawa, who explains three of his colleagues investigating the Saeki deaths all were consumed by the curse. That night, Nakagawa goes to the house and tries to burn it down, but is killed by Takeo.
Karen races to the house upon learning Doug has ventured there to look for her, experiencing a vision in which she sees Peter visiting the house and finding Kayako's corpse. Karen finds Doug paralyzed by fear, and attempts to flee the house with him, only to witness Kayako as she drags herself down the stairs and crawls on Doug, causing him to die of fright. Karen spots the petrol and manages to ignite it with Doug's lighter just as Kayako is about to kill her. Karen is whisked to a hospital, but learns the house survived the fire. Visiting Doug's body, Karen realizes she is still haunted by Kayako, who appears behind her as the camera circles to reveal her wide staring eye.

Question: who murdered his wife?
Answer: Saeki.