  We develop a new nonparametric method to reconstruct the Equation of State
(EoS) of Neutron Star with multimessenger data. As an universal function
approximator, the Feed-Forward Neural Network (FFNN) with one hidden layer and
a sigmoidal activation function can approximately fit any continuous function.
Thus we are able to implement the nonparametric FFNN representation of the
EoSs. This new representation is validated by its capabilities of fitting the
theoretical EoSs and recovering the injected parameters. Then we adopt this
nonparametric method to analyze the real data, including mass-tidal
deformability measurement from the Binary Neutron Star (BNS) merger
Gravitational Wave (GW) event GW170817 and mass-radius measurement of PSR
J0030+0451 by {\it NICER}. We take the publicly available samples to construct
the likelihood and use the nested sampling to obtain the posteriors of the
parameters of FFNN according to the Bayesian theorem, which in turn can be
translated to the posteriors of EoS parameters. Combining all these data, for a
canonical 1.4 $M_\odot$ neutron star, we get the radius
$R_{1.4}=11.83^{+1.25}_{-1.08}$ km and the tidal deformability $\Lambda_{1.4} =
323^{+334}_{-165}$ (90\% confidence interval).Furthermore, we find that in the
high density region ($\geq 3\rho_{\rm sat}$), the 90\% lower limits of the
$c_{\rm s}^2/c^2$ ($c_{\rm s}$ is the sound speed and $c$ is the velocity of
light in the vacuum) are above $1/3$, which means that the so-called conformal
limit (i.e., $c_{\rm s}^2/c^2<1/3$) is not always valid in the neutron stars.
