diff --git a/base/parse.jl b/base/parse.jl
index 50b76e0577eb1..ecbfdbe3f92b1 100644
--- a/base/parse.jl
+++ b/base/parse.jl
@@ -73,7 +73,7 @@ function parseint_preamble(signed::Bool, base::Int, s::AbstractString, startpos:
     (j == 0) && (return 0, 0, 0)
 
     if base == 0
-        if c == '0' && i <= ncodeunits(s)
+        if c == '0' && i <= endpos
             c, i = iterate(s,i)::Tuple{Char, Int}
             base = c=='b' ? 2 : c=='o' ? 8 : c=='x' ? 16 : 10
             if base != 10
diff --git a/test/parse.jl b/test/parse.jl
index c3b49ebdc7e1c..5bf3b806edca8 100644
--- a/test/parse.jl
+++ b/test/parse.jl
@@ -30,6 +30,16 @@
 @test_throws ArgumentError parse(Int, 'a')
 @test_throws ArgumentError parse(Int,typemax(Char))
 
+# Issue 29451
+struct Issue29451String <: AbstractString end
+Base.ncodeunits(::Issue29451String) = 12345
+Base.lastindex(::Issue29451String) = 1
+Base.isvalid(::Issue29451String, i::Integer) = i == 1
+Base.iterate(::Issue29451String, i::Integer=1) = i == 1 ? ('0', 2) : nothing
+
+@test Issue29451String() == "0"
+@test parse(Int, Issue29451String()) == 0
+
 # Issue 20587
 for T in Any[BigInt, Int128, Int16, Int32, Int64, Int8, UInt128, UInt16, UInt32, UInt64, UInt8]
     T === BigInt && continue # TODO: make BigInt pass this test