No. It is actually lighter than air.
You can work this out from the fact that a gas’s density is proportional to its formula mass.
If we take the atomic masses of Carbon (C) as 12, Hydrogen (H) as 1, Oxygen (O) as 16 and Nitrogen (N) as 14 then:
Air contains Nitrogen (N2) – 78% and oxygen (O2) 21%. The equivalent ‘formula mass’ of air is therefore just slightly more than 28 (2 x14)
Methane’s (CH4) formula mass is 12+ 4 or just 16 – so it is lighter than air as the formula mass (and hence density) is less than 28.
[I haven't referenced this as stefanthedenier doesn't believe in references]