A random-primed reverse transcriptase-in vitro transcription method of linearly amplifying RNA is provided. According to the methods of the invention, source RNA (or other single-stranded nucleic acid), preferably, mRNA, is converted to double-stranded cDNA using two random primers, one of which comprises a RNA polymerase promoter sequence ("promoter-primer"), to yield a double-stranded cDNA that comprises a RNA polymerase promoter that is recognized by a RNA polymerase. Preferably, the primer for first-strand cDNA synthesis is a promoter-primer and the primer for second-strand cDNA synthesis is not a promoter-primer. The double-stranded cDNA is then transcribed into RNA by the RNA polymerase, optimally in the presence of a reverse transcriptase that is rendered incapable of RNA-dependent DNA polymerase activity during this transcription step. The subject methods produce linearly amplified RNA with little or no 3' bias in the sequences of the nucleic acid population amplified.