Let
T
\mathcal {T}
be a tetrahedral mesh. We present a 3-D local refinement algorithm for
T
\mathcal {T}
which is mainly based on an 8-subtetrahedron subdivision procedure, and discuss the quality of refined meshes generated by the algorithm. It is proved that any tetrahedron
T
∈
T
\mathbf {T} \in \mathcal {T}
produces a finite number of classes of similar tetrahedra, independent of the number of refinement levels. Furthermore,
η
(
T
i
n
)
≥
c
η
(
T
)
\eta (\mathbf {T}_i^{n}) \geq c \eta (\mathbf {T})
, where
T
∈
T
\mathbf {T} \in \mathcal {T}
,
c
c
is a positive constant independent of
T
\mathcal {T}
and the number of refinement levels,
T
i
n
\mathbf {T}_i^{n}
is any refined tetrahedron of
T
\mathbf {T}
, and
η
\eta
is a tetrahedron shape measure. It is also proved that local refinements on tetrahedra can be smoothly extended to their neighbors to maintain a conforming mesh. Experimental results show that the ratio of the number of tetrahedra actually refined to the number of tetrahedra chosen for refinement is bounded above by a small constant.