We establish the existence of a scaling limit
E
p
\mathcal {E}_p
of discrete
p
p
-energies on the graphs approximating a generalized Sierpiński carpet for
p
>
d
A
R
C
p > d_{\mathrm {ARC}}
, where
d
A
R
C
d_{\mathrm {ARC}}
is the Ahlfors regular conformal dimension of the underlying generalized Sierpiński carpet. Furthermore, the function space
F
p
\mathcal {F}_{p}
defined as the collection of functions with finite
p
p
-energies is shown to be a reflexive and separable Banach space that is dense in the set of continuous functions with respect to the supremum norm. In particular,
(
E
2
,
F
2
)
(\mathcal {E}_2, \mathcal {F}_2)
recovers the canonical regular Dirichlet form constructed by Barlow and Bass [Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), pp. 225–257] or Kusuoka and Zhou [Probab. Theory Related Fields 93 (1992), pp. 169–196]. We also provide
E
p
\mathcal {E}_{p}
-energy measures associated with the constructed
p
p
-energy and investigate its basic properties like self-similarity and chain rule.