A total of 24,473 attempts were made since last June's general election from devices connected to the parliamentary network, according to data obtained by a PA Freedom of Information (FOI) request.
Prime Minister Theresa May is already reeling from a wave of sexual misconduct allegations in Westminster.
She was forced to dump minister and long-time friend Damian Green last month after he apparently misled police over claims pornography was found on computers in his Westminster office in 2008.
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The parliamentary internet network is used by MPs, Lords in the upper house and their staff.
Authorities claim most attempts are not deliberate and point to a decrease in recent years.
Parliament blocked 113,208 attempts in 2016, down from 213,020 the previous year.
"All pornographic websites are blocked by parliament's computer network," a parliamentary spokesman told PA.
"The vast majority of 'attempts' to access them are not deliberate.
"This data also covers personal devices used when logged on to parliament's guest Wi-Fi."
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