  Millimeter sized single crystals of CaFe$_{1-x}$Co$_x$AsF were grown using a
self-flux method. It is found that high-quality single crystals can be grown
from three approaches with different initial raw materials. The chemical
compositions and crystal structure were characterized carefully. The c-axis
lattice constant is suppressed by the Co substitution. Superconductivity with
the critical transition $T_c$ as high as 21 K was confirmed by both the
resistivity and magnetic susceptibility measurements in the sample with $x$ =
0.12. Moreover, it is found that $T_c$ can be enhanced for about 1 K under the
very small hydrostatic pressure of 0.22 GPa, which is more quickly than that
reported in the polycrystalline samples. Our results is a promotion for the
physical investigations of 1111 phase iron-pnictide superconductors.
