diff --git a/src/Approximations/box_approximation.jl b/src/Approximations/box_approximation.jl
index 3af7ed161a..e7f372bec7 100644
--- a/src/Approximations/box_approximation.jl
+++ b/src/Approximations/box_approximation.jl
@@ -54,6 +54,9 @@ function box_approximation(S::LazySet{N}) where {N}
     r = Vector{N}(undef, n)
     @inbounds for i in 1:n
         lo, hi = extrema(S, i)
+        if isinf(lo) || isinf(hi)
+            throw(ArgumentError("the box approximation of an unbounded set is undefined"))
+        end
         ri = (hi - lo) / 2
         if ri < zero(N)
             if !_geq(ri, zero(N))
diff --git a/test/Sets/Line.jl b/test/Sets/Line.jl
index a245e9e0f1..004161e92e 100644
--- a/test/Sets/Line.jl
+++ b/test/Sets/Line.jl
@@ -46,6 +46,9 @@ for N in [Float64, Rational{Int}, Float32]
     # boundedness
     @test !isbounded(l1)
 
+    # box_approximation
+    @test_throws ArgumentError box_approximation(l1)
+
     # ispolyhedral
     @test ispolyhedral(l1)