  In the manuscript, we discuss properties of SDSS J1451+2709, a normal blue
quasar but mis-classified as a HII galaxy in the BPT diagram (called as a
mis-classified quasar). The emission lines around H$\alpha$ and H$\beta$ are
well measured by different model functions with broad Balmer lines being
described by Gaussian or Lorentz functions, in the SDSS spectrum in 2007 and in
the KPNO spectrum in 1990. After considering variations of broad emission
lines, different model functions lead to different fluxes of narrow emission
lines, but the different narrow emission line flux ratios lead the SDSS
J1451+2709 to be classified as a HII galaxy in the BPT diagram. In order to
explain the unique properties of the mis-classified quasar SDSS J1451+2709 in
the BPT diagram, two methods are proposed, the starforming contributions and
compressed NLRs with high electron densities near to critical densities of
forbidden emission lines. Unfortunately, the two methods cannot be preferred in
the SDSS J1451+2709, further efforts are necessary to find the physical origin
of the unique properties of the mis-classified quasar SDSS J1451+2709 in the
BPT diagram. Meanwhile, there are not quite different long-term variabilities
of SDSS J1451+2709 from the normal quasars. The mis-classified quasar SDSS
J1451+2709, an extremely unique case or a special case among the normal
quasars, could provide further clues on the applications of BPT diagrams to the
normal broad line AGN and to narrow emission line objects, indicating part of
narrow emission line HII galaxies actually harbouring central AGN activities.
