  Measuring the Higgs self-coupling is one of the crucial physics goals at the
LHC Run-2 and other future colliders. In this work, we attempt to figure out
the size of SUSY effects on the trilinear self-coupling of the 125 GeV Higgs
boson in the MSSM and NMSSM after the LHC Run-1. Taking account of current
experimental constraints, such as the Higgs data, flavor constraints,
electroweak precision observables and dark matter detections, we obtain the
observations: (1) In the MSSM, the ratio of
$\lambda^{MSSM}_{3h}/\lambda^{SM}_{3h}$ has been tightly constrained by the LHC
data, which can be only slightly smaller than 1 and minimally reach 97\%; (2)
In the NMSSM with $\lambda<0.7$, a sizable reduction of
$\lambda^{NMSSM}_{3h_2}/\lambda^{SM}_{3h_2}$ can occur and minimally reach 10\%
when the lightest CP-even Higgs boson mass $m_{h_1}$ is close to the SM-like
Higgs boson $m_{h_2}$ due to the large mixing angle between the singlet and
doublet Higgs bosons; (3) In the NMSSM with $\lambda>0.7$, a large enhancement
or reduction $-1.1<\lambda^{NMSSM}_{3h_1}/\lambda^{SM}_{3h_1}<2$ can occur,
which is accompanied by a sizable change of $h_1\tau^+\tau^-$ coupling. The
future colliders, such as the HL-LHC and ILC, will have the capacity to test
these large deviations in the NMSSM.
