  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 functions.
We thus implement the FFNN to construct the EoSs, by fitting the theoretical
EoSs and recovering the injected parameters, and find it perform well. Then we
apply this nonparametric method to analyzing 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
hyper 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
$R_{1.4}=11.87^{+1.21}_{-1.06}$ km and the tidal deformability $\Lambda_{1.4} =
329^{+322}_{-163}$ (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 larger than 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.
