The second degree of a vertex in a simple graph is defined as the number of its second neighbors. The leap eccentric connectivity index of a graph
M
,
L
ξ
c
M
, is the sum of the product of the second degree and the eccentricity of every vertex in
M
. In this paper, some lower and upper bounds of
L
ξ
c
S
M
in terms of the numbers of vertices and edges, diameter, and the first Zagreb and third leap Zagreb indices are obtained. Also, the exact values of
L
ξ
c
S
M
for some well-known graphs are computed.