We discuss the possibility of using the frequency-chirping technique to shorten the duration of the generated single attosecond pulse (SAP) by a two-color laser field of 800 and 1600 nm with few-cycle pulses. By adopting various combinations of the two frequency-chirped laser fields in our numerical simulation of ionizing He atom, we demonstrate that the best possible condition to obtain the shortest SAP is using the same chirping in both the fundamental and the half-harmonic laser fields without any phase effect and any delay time. There is a maximum increment of about 40 eV in the bandwidth of the XUV super-continuum in the cutoff (the second plateau) region. A single isolated attosecond pulse of 48 as can be generated that is further reduced to 9.7 as by phase compensation. (C) 2011 Elsevier B. V. All rights reserved.