diff --git a/spacy/displacy/render.py b/spacy/displacy/render.py
index 8e980d203..fb25b60e2 100644
--- a/spacy/displacy/render.py
+++ b/spacy/displacy/render.py
@@ -6,6 +6,8 @@ import uuid
 from .templates import TPL_DEP_SVG, TPL_DEP_WORDS, TPL_DEP_ARCS, TPL_ENTS
 from .templates import TPL_ENT, TPL_ENT_RTL, TPL_FIGURE, TPL_TITLE, TPL_PAGE
 from ..util import minify_html, escape_html, get_entry_points
+from ..errors import Errors
+
 
 DEFAULT_LANG = "en"
 DEFAULT_DIR = "ltr"
@@ -124,6 +126,9 @@ class DependencyRenderer(object):
         i (int): Unique ID, typically arrow index.
         RETURNS (unicode): Rendered SVG markup.
         """
+        if start < 0 or end < 0:
+            error_args = dict(start=start, end=end, label=label, dir=direction)
+            raise ValueError(Errors.E156.format(**error_args))
         level = self.levels.index(end - start) + 1
         x_start = self.offset_x + start * self.distance + self.arrow_spacing
         if self.direction == "rtl":
diff --git a/spacy/errors.py b/spacy/errors.py
index d23ad66e8..e8027f2cf 100644
--- a/spacy/errors.py
+++ b/spacy/errors.py
@@ -428,6 +428,10 @@ class Errors(object):
     E154 = ("Either the `nlp` model or the `vocab` should be specified.")
     E155 = ("The `nlp` object should have access to pre-trained word vectors, cf. "
             "https://spacy.io/usage/models#languages.")
+    E156 = ("Can't render negative values for dependency arc start or end. "
+            "Make sure that you're passing in absolute token indices, not "
+            "relative token offsets.\nstart: {start}, end: {end}, label: "
+            "{label}, direction: {dir}")
 
 
 @add_codes
diff --git a/spacy/tests/test_displacy.py b/spacy/tests/test_displacy.py
index 2097fd081..5e99d261a 100644
--- a/spacy/tests/test_displacy.py
+++ b/spacy/tests/test_displacy.py
@@ -3,6 +3,7 @@ from __future__ import unicode_literals
 
 import pytest
 from spacy import displacy
+from spacy.displacy.render import DependencyRenderer
 from spacy.tokens import Span
 from spacy.lang.fa import Persian
 
@@ -42,6 +43,17 @@ def test_displacy_parse_deps(en_vocab):
     ]
 
 
+def test_displacy_invalid_arcs():
+    renderer = DependencyRenderer()
+    words = [{"text": "This", "tag": "DET"}, {"text": "is", "tag": "VERB"}]
+    arcs = [
+        {"start": 0, "end": 1, "label": "nsubj", "dir": "left"},
+        {"start": -1, "end": 2, "label": "det", "dir": "left"},
+    ]
+    with pytest.raises(ValueError):
+        renderer.render([{"words": words, "arcs": arcs}])
+
+
 def test_displacy_spans(en_vocab):
     """Test that displaCy can render Spans."""
     doc = get_doc(en_vocab, words=["But", "Google", "is", "starting", "from", "behind"])