  We calculate contributions to $B_s-\bar{B}_s$ mixing through tree-level
sneutrino exchange in the framework of the minimal supersymmetric standard
model with R-parity violation, including the next-to-leading-order QCD
corrections. We compare our results with the updated bounds on the
$B_s-\bar{B}_s$ mass difference reported by CDF collaborations, and present new
constraints on the relevant combinations of parameters of the minimal
supersymmetric standard model with R-parity violation. Our results show that
upper bound on the relevant combination of couplings of $B_s-\bar{B}_s$ mixing
is of the order $10^{-9}$. We also calculate the $B^0_d-\bar{B}^0_d$ and
$K^0-\bar{K}^0$ mass differences, and show that the upper bounds on the
relevant combinations of couplings are two and four orders of magnitude
stronger than ones reported in the literatures, respectively. We also discuss
the case of complex couplings and show that how the relevant combinations of
couplings are constrained by the updated experiment data of $B_s-\bar{B}_s$,
$B_d-\bar{B}_d$ mixing and time-dependent CP asymmetry $S_{J/\psi K_s}$, and
future possible observations of $S_{J/\psi\phi}$ at LHCb, respectively.
