The party claims it could save £14m over the next four years by reducing councillor numbers.
It wants planning and environment issues passed town and parish councils while a Yorkshire parliament deals with areas such as transport, policing and education.
The party wants Yorkshire to have the power to set its own tax rates and abolish police and crime commissioners.
Party leader Richard Carter said: “In Yorkshire we can only look on jealously as Scotland, Wales, Northern Ireland and even London have elections in May to local decision making bodies to help make local decisions.
“Yorkshire won’t have those elections but we have nevertheless outlined a vision of how our region might look with a devolved parliament.
“We are clear, we’re not calling for devolution for devolution’s sake. We’re calling for devolution because our schools, infrastructure and economy deserve better.”
Mr Carter added: “The debate is now not whether Yorkshire should have more decision making powers. Instead, it is about what powers our region should have and how these should be used.”
The Yorkshire First manifesto wants a “Yorkshire Educational Challenge” to drive up standards in the region’s schools modelled on similar initiative in London.
It also wants those in flood prone areas not to have to pay insurance premium tax, investment in broadband for rural areas and more affordable housing in the countryside.
The local elections are being held on Thursday, May 5.