The party is seeking approval from the cantonal parliament for a feasibility study into such a people-moving system outside the city centre.
The Greens envisage two lines, including one that would link Geneva's airport and Bernex, a western suburb with several stops along the way, including Balexert, the canton's largest shopping centre.
According to information presented by the party, the cable cars would travel at 22 kilometres an hour, meaning that the trip from Bernex to the airport would take 20 minutes.
Another proposed line would cross the Rhône River to link Le Lignon, a residential suburb with a forested park and the Vernets ice skating rink.
The Greens say the system could connect with existing tram lines and a new regional railway (CEVA) under construction to link Geneva's main train station with communities in neighbouring France.
And residential buildings could be created to serve as pylons to hold up the cable car.
The Greens expect critics to poke fun at the idea.
But party MP François Lefort, sponsor of the motion for the study, recalled that people laughed when mountain lifts were first proposed in Switzerland at the end of the 19th century, the Tribune de Genève newspaper reported.
“Public transport by cable exists now in 16 countries and 36 cities,” André Baud, a Green politician in the municipality of Bernex, told the Tribune.
“It allows to overcome obstacles (that other forms of transport cannot) and it benefits from a very high rate of use.”
Cities such as Barcelona, Grenoble and Caracas are among those that use cable cars in urban areas.
Lefort admitted to being sceptical about such systems but he became convinced of the advantages, he told the Tribune.
Cable cars require three and a half times less energy than streetcars while they occupy much less ground-level space, proponents say.
They are also easy and economic to build and they require little staffing to operate.
And they can be installed virtually anywhere, crossing rivers, rocky outcroppings and highways.
While they can carry fewer passengers than streetcars and buses, they are well-suited to suburban areas, Lefort said.