A Horse with No Name was recorded by America and released in 1971, which decade did the band gain popularity? 
A Horse with No Name:  It was the band's first and most successful single, released in late-1971 in Europe and early-1972 in the US, and topped the charts in several countries. America (band): America achieved significant popularity in the 1970s and was famous for the trio's close vocal harmonies and light acoustic folk rock sound.
in the 1970s