The study of B physics plays a fundamental role both in accurately testing the Standard Model and in search of new physics. For such purpose, it is very import to determine the B -meson transition matrix elements with high accuracy. Especially, as has already been emphasized in many works in the literature, the simplest matrix element f$_{B}$ , which is defined as 〈 0 | ¯ qγ$_{µ}$γ$_{5}$b | B ( p ) 〉 = if$_{B}$p$_{µ}$ or ( m$_{b}$ + m$_{q}$ ) 〈 0 | ¯ qiγ$_{5}$b | B ( p ) 〉 = m 2 $_{B}$f$_{B}$ is fundamental for the physics of the heavy-light quark systems, where q denotes the light u or d quark under the isospin symmetry. The decay constants usually are studied through their leptonic decays, earlier discussions of which can be found in Ref.[1]. As for f$_{B}$ , its first direct measurement is done by Belle experiment, which shows that f$_{B}$ = 229 +36 − $_{31}$(stat) +34 − $_{37}$(syst) MeV from the measurement of the decay B − → τ ¯ ν$_{τ}$ [2]. At the present, the lattice QCD calculation and the QCD sum rules are two suitable approaches for theoretically extracting these elements and their results are usually complementary to each other. Some typical extractions of f$_{B}$ were investigated in Refs.[3–11] from QCD sum rules and in Refs.[12–17] from lattice calculation. The QCD sum rules approach was developed by Shifman, Vainshtein and Zakharov (SVZ) in the seventies of last century [18], and now, it becomes a widely adopted tool for studying hadron phenomenology. It was designed to determine the properties of the ground-state hadrons at low momentum transfer to the region of large momentum transfer. More explic- itly, hadrons are represented by certain interpolating quark currents taken at large virtuality, and then the correlation function (correlator) of these currents is introduced and treated in the framework of operator product expansion (OPE) such that the short- and the long- distance quark-gluon interactions are separated. The short-distance interaction is calcu- lated using perturbative QCD, while the long-distance one can be parameterized in terms of the universal non-perturbative vacuum condensates. Next, the result of QCD calcula- tion is matched, via dispersion relation, to a sum over hadronic states. Finally, the Borel transformation is introduced to suppress or even cut off the irrelevant or unknown excited and continuum states so as to improve the accuracy of the obtained sum rules, since little is known about the spectral function of the excited and continuum states. In such a way, the so called SVZ sum rules combines the concepts of OPE, the dispersive representation of correlator and the quark-hadron duality consistently that allows the derived non-excited hadron states’ properties to be within their reasonable theoretical uncertainties. It is noted that one of the basic quantity for the QCD sum rules is the correlator. How to “design” a proper correlator for a particular case is a tricky problem. By a suitable choice of 2