I. INTRODUCTION It has been more than ten years since our universe was found to be in accelerating expansion [1]. A dominated and uniformly distributed energy component of the universe, called dark energy (DE), should be responsible for the acceleration. Many DE models have been proposed [2–6]. The simplest cosmological model is ΛCDM model, which contains a cosmological constant as dark energy. While ΛCDM model is still consistent well with all observational data, a lot of efforts have been made to find out whether DE is time-evolving or is just the cosmological constant. To do that, several parameterizations of equation of state (EoS) of DE have been proposed to fit with observational data, such as the ansatz w$_{de}$ = w$_{0}$ + w $^{′}$z [7], the EoS expanded by redshift, and the CPL parametrization [8, 9] w$_{de}$ = w$_{0}$ + w$_{a}$z/ (1+ z ), expanded by scale factor. Both of them contain two free parameters: w$_{0}$ , the present value of EoS, and w ′ or w$_{a}$ , represents the time evolution of EoS. Clearly, constraints of EoS obtained by using these parameterizations are model-dependent. Given an unreal assumption of EoS of DE, one may lead to wrong conclusions. Some model- independent methods have also been proposed [10–13], such as the widely-used uncorrelated bandpower estimates (UBE) [11, 14], in which the redshift is binned and w$_{de}$ is assumed as a constant in each redshift bin. Note that the UBE method just approximates the actual w$_{de}$ by an averaged constant in each bin if DE is dynamical. If there are sufficient data, w$_{de}$ ( z ) can be accurately reconstructed. However, current data could only support a few bins, thus UBE is always used to test the deviation of w$_{de}$ from the cosmological constant and used as a supplementary for the parameterizations of w$_{de}$ . Note that the cubic-spline interpolation has also been proposed to study the binned w$_{de}$ ( z ) [15, 16]. However, no convincing evidence of dynamic DE has been found [15–17]. In addition, let us note that the ansatz, w$_{de}$ = w$_{0}$ + w $^{′}$z , of redshift expansion and CPL parametrization exclude the possibility of an oscillation EoS, if they are used to fit the whole expansion history of the universe. While the UBE method needs enough bins to reveal the real dynamical behavior of DE, the errors will get larger as the number of bins increases. In this paper, we would like to probe the dynamical behavior of w$_{de}$ by using the linear- spline method. We will approximate w$_{de}$ in each redshift bin by a linear function w = w$_{0}$ + w $^{′}$z , and require that w$_{de}$ ( z ) is continuous in the region under consideration. Since most of data we used (e.g., SnIa data) are in low redshift, we will focus on the region of low 2