  We point out that the CPL parametrization has a problem that the equation of
state $w(z)$ diverges in the far future, so that this model can only properly
describe the past evolution but cannot depict the future evolution. To overcome
such a difficulty, in this Letter we propose two novel parametrizations for
dark energy, the logarithm form $w(z)=w_0+w_1({\ln (2+z)\over 1+z}-\ln2)$ and
the oscillating form $w(z)=w_0+w_1({\sin(1+z)\over 1+z}-\sin(1))$, successfully
avoiding the future divergency problem in the CPL parametrization, and use them
to probe the dynamics of dark energy in the whole evolutionary history. Our
divergency-free parametrizations are proven to be very successful in exploring
the dynamical evolution of dark energy and have powerful prediction capability
for the ultimate fate of the universe. Constraining the CPL model and the new
models with the current observational data, we show that the new models are
more favored. The features and the predictions for the future evolution in the
new models are discussed in detail.
