The union's General Secretary Mick Cash told the media that his members were facing public anger "without a shred of support" from Grayling or Northern's management.
The move came as the railway company had cancelled over 200 services with other services being affected, Xinhua news agency reported.
This constituted part of passengers' frustration as they had to face widespread cancellations and delays since the timetable change was adopted on May 20. Grayling has not responded to the resign call.
Greater Manchester Mayor Andy Burnham told the BBC he understands Northern will introduce an emergency timetable.
A spokesman for Northern said there will be "amended services" from Monday. Since May 18, more than 2,000 Northern services have been aborted.
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