We examine the clustering of quasars over a wide luminosity range, by utilizing 901 quasars at $overline{z}_{rm phot}sim3.8$ with $-24.73<M_{rm 1450}<-22.23$ photometrically selected from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) S16A Wide2 date release and 342 more luminous quasars at $3.4<z_{rm spec}<4.6$ having $-28.0<M_{rm 1450}<-23.95$ from the Sloan Digital Sky Survey (SDSS) that fall in the HSC survey fields. We measure the bias factors of two quasar samples by evaluating the cross-correlation functions (CCFs) between the quasar samples and 25790 bright $zsim4$ Lyman Break Galaxies (LBGs) in $M_{rm 1450}<-21.25$ photometrically selected from the HSC dataset. Over an angular scale of timeform{10.0} to timeform{1000.0}, the bias factors are $5.93^{+1.34}_{-1.43}$ and $2.73^{+2.44}_{-2.55}$ for the low and high luminosity quasars, respectively, indicating no luminosity dependence of quasar clustering at $zsim4$. It is noted that the bias factor of the luminous quasars estimated by the CCF is smaller than that estimated by the auto-correlation function (ACF) over a similar redshift range, especially on scales below timeform{40.0}. Moreover, the bias factor of the less-luminous quasars implies the minimal mass of their host dark matter halos (DMHs) is $0.3$-$2times10^{12}h^{-1}M_{odot}$, corresponding to a quasar duty cycle of $0.001$-$0.06$.
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