James Bray, 24, of Southend, Essex, had previously admitted three animal cruelty offences following the incident at 3am on January 18.
The two-year-old Staffordshire Bull terrier, named Beano, died after being thrown from the window at the block of flats where Bray lived, the RSPCA said.
Bray claimed the dog had been ''playing up'' by urinating on the carpet and had bared its teeth at him.
He had tied Beano up in the bathroom for four hours. When he released him, the dog had been aggressive so he tossed him out of the window, the charity added.
A spokesman said: ''He then called the police to tell them he had done it and they found Beano's body on the ground at the base of the flats - he had died on impact.''
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Bray had owned Beano for two months.
Today at Southend Magistrates' Court he was jailed for two months and sentenced to a further two months on community licence.
He was fined £500 and given a life ban on keeping any animal.
RSPCA inspector Matt Gough said: ''It is inexplicable that someone would do this - even if the dog had attacked him, there is no excuse for throwing it out of the window.
''We are pleased that the magistrates have given him a lifetime ban on keeping animals.''
The court heard that Bray was diagnosed with paranoid schizophrenia after the incident.