An adaptor for use in amplifying all linear, double-stranded nucleic acid molecules of unknown sequences in a sample is disclosed. The adaptor consists of: (1) the first oligonucleotide (P-oligo) with a phosphate at the 5′ end and without an additional thymine nucleotide at the 3′ end; and (2) the second oligonucleotide (T˜oligo) with an extra 3′-T and without a 5′-phosphate. The P-oligo and T-oligo are complementary to each other except at the 3′-T (thymine) in the T-oligo. The adaptor is ligated to nucleic acids of unknown sequences which have an extra A in the 3′ end (3′˜A overhang) to form adaptor-ligated target nucleic acids. The T-oligo is then employed as a single primer for T-oligo-primed polymerase chain reaction (TOP-PCR) and amplifies the nucleic acids of unknown sequences in full-length.