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Mumbai to Goa by Road: There are two major routes connecting Mumbai with Goa. The first is along NH17 and the second is via Pune (NH4).

Mumbai to Goa distance (via NH4) 600km : Mumbai - 150km-> Pune -450km-> Goa (Panjim)
Mumbai to Goa distance (via NH17) 650km : Mumbai -560km-> Goa (Panjim)

Though the second route (NH17) is shorter, doesn't necessarily means you'll reach Goa faster. NH17 is a curvy but well made highway whereas NH4 is part of the Golden Quadrilateral (GQ) with 4/6 lanes most of the time, till you make that final diversion around Belgaum towards Goa. Also note NH4 route is with frequent tolls, you'll shell out about Rs500 between Mumbai and Goa.

Purists among the road junkies will like the curvy drive on the NH17. It's a scenic route. NH4 route is no nonsense route, another typical newly built highway.

There are many pros and cons between these two routes. See the comparison between the NH17 & HN4 options to travel between Mumbai and Goa.

Also See Mumbai to Goa route via Pune

Mumbai to Goa by Bus: 

There is a plethora of private operators do daily bus service between various   places in Mumbai and Goa.  Fare ranges from anything from Rs600 to Rs2500.

Go for the upscale type services (Volvo Sleeper) if you are looking for comfortable overnight journey. Between the bus and Train options, prefer train as it is any day more comfortable than the 12-14 hours of locked up bus journey.

Check with ticketing sites like redbus.in, makemytrip.com, cleartrip.com etc for prices and seat availability.

Mumbai to Goa Trains :

There are at least 10 express trains that connect Mumbai with Goa. Some are daily express trains while the rest are weekly or biweekly trains. See the timetable below to find the train operations.

The southbound Mangalore Express (Train No : 12133) is probably the most convenient overnight train to travel from  Mumbai to Goa. Mangalore Express leaves Mumbai CST station (Station Code: CSTM) by 10pm and reaches Goa's Madgaon (Station Code : MAO) by 7 in the morning. There are also other popular trains between  Mumbai and Goa like the Mandovi Express, Konkan Kanya Express etc.

See more about Mumbai to Goa train options to select the best suited train to your plan.

Mumbai to Goa by Flight: It's an one hour flight between Mumbai and Goa. You should be able to book a round trip ticket for about Rs6000 (or even less) if booked reasonably in advance.

Prices do get jacked up even 5 times during the much sought after New Year eve periods. Indigo, Jet Airways, Spice Jet, Indian Airlines operate many day flights to Goa.

Mumbai to Goa by Ship : No, those ferry services between Mumbai port and Goa do not exist anymore.

You may find cruise lines operating as packaged tours though.  There are some plans to revive the Mumbai-Goa ferry service.

But till then you will need to depend on rail, road or air routes.