We study the low-degree solution of the Sylvester matrix equation
A
1
λ
+
A
0
X
λ
+
Y
λ
B
1
λ
+
B
0
=
C
0
, where
A
1
λ
+
A
0
and
B
1
λ
+
B
0
are regular. Using the substitution of parameter variables
λ
, we assume that the matrices
A
0
and
B
0
are invertible. Thus, we prove that if the equation is solvable, then it has a low-degree solution
L
λ
,
M
λ
, satisfying the degree conditions
δ
L
λ
<
Ind
A
0
−
1
A
1
and
δ
M
λ
<
Ind
B
1
B
0
−
1
.