  The convergence peaks, constructed from galaxy shape measurement in weak
lensing, is a powerful probe of cosmology as the peaks can be connected with
the underlined dark matter haloes. However the capability of convergence peak
statistic is affected by the noise in galaxy shape measurement, signal to noise
ratio as well as the contribution from the projected mass distribution from the
large-scale structures along the line of sight (LOS). In this paper we use the
ray-tracing simulation on a curved sky to investigate the correspondence
between the convergence peak and the dark matter haloes at the LOS. We find
that, in case of no noise and for source galaxies at $z_{\rm s}=1$, more than
$65\%$ peaks with $\text{SNR} \geq 3$ (signal to noise ratio) are related to
more than one massive haloes with mass larger than $10^{13} {\rm M}_{\odot}$.
Those massive haloes contribute $87.2\%$ to high peaks ($\text{SNR} \geq 5$)
with the remaining contributions are from the large-scale structures. On the
other hand, the peaks distribution is skewed by the noise in galaxy shape
measurement, especially for lower SNR peaks. In the noisy field where the shape
noise is modelled as a Gaussian distribution, about $60\%$ high peaks
($\text{SNR} \geq 5$) are true peaks and the fraction decreases to $20\%$ for
lower peaks ($ 3 \leq \text{SNR} < 5$). Furthermore, we find that high peaks
($\text{SNR} \geq 5$) are dominated by very massive haloes larger than $10^{14}
{\rm M}_{\odot}$.
