  We present results of our theoretical investigation of double-parton
scattering (DPS) effects in production of heavy flavour mesons (charm and
bottom). We discuss production of charm-bottom and bottom-bottom meson-meson
pairs in proton-proton collisions at the LHC. The calculation of DPS mechanism
is performed within factorized ansatz where each parton scattering is
calculated in the framework of the $k_T$-factorization. The hadronization is
done with the help of independent parton fragmentation picture. For
completeness we compare results for double- and single-parton scattering (SPS).
As in the case of double charm production also here the DPS dominates over the
SPS, especially for small transverse momenta. We present several distributions
and integrated cross sections with realistic cuts for simultaneous production
of $D^0 B^+$ and $B^+ B^+$, suggesting future experimental studies at the LHCb
detector.
