In this paper, over imaginary quadratic fields, we consider the family of
L
L
-functions
L
(
s
,
f
)
L (s, f)
for an orthonormal basis of spherical Hecke–Maass forms
f
f
with Archimedean parameter
t
f
t_f
. We establish asymptotic formulae for the twisted first and second moments of the central values
L
(
1
2
,
f
)
L\big (\frac 1 2, f\big )
, which can be applied to prove that at least
33
33 %
of
L
(
1
2
,
f
)
L\big (\frac 1 2, f\big )
with
t
f
⩽
T
t_f \leqslant T
are non-vanishing as
T
→
∞
T \rightarrow \infty
. Our main tools are the spherical Kuznetsov trace formula and the Voronoï summation formula over imaginary quadratic fields.