diff --git a/src/PhpSpreadsheet/Reader/Xls.php b/src/PhpSpreadsheet/Reader/Xls.php
index 6b4be6d90..4b4a8e484 100644
--- a/src/PhpSpreadsheet/Reader/Xls.php
+++ b/src/PhpSpreadsheet/Reader/Xls.php
@@ -2116,7 +2116,9 @@ class Xls extends BaseReader
                 // check the OpenOffice documentation of the FONT record
                 $fontIndex = self::getUInt2d($recordData, 0) - 1;
             }
-            $objStyle->setFont($this->objFonts[$fontIndex]);
+            if (isset($this->objFonts[$fontIndex])) {
+                $objStyle->setFont($this->objFonts[$fontIndex]);
+            }
 
             // offset:  2; size: 2; Index to FORMAT record
             $numberFormatIndex = self::getUInt2d($recordData, 2);
diff --git a/tests/PhpSpreadsheetTests/Reader/Xls/XlsBugPr3734Test.php b/tests/PhpSpreadsheetTests/Reader/Xls/XlsBugPr3734Test.php
new file mode 100644
index 000000000..85bfbfb76
--- /dev/null
+++ b/tests/PhpSpreadsheetTests/Reader/Xls/XlsBugPr3734Test.php
@@ -0,0 +1,23 @@
+<?php
+
+declare(strict_types=1);
+
+namespace PhpOffice\PhpSpreadsheetTests\Reader\Xls;
+
+use PhpOffice\PhpSpreadsheet\IOFactory;
+use PHPUnit\Framework\TestCase;
+
+class XlsBugPr3734Test extends TestCase
+{
+    /**
+     * Test XLS file including data with missing fonts?
+     */
+    public function testXlsFileWithNoFontIndex(): void
+    {
+        $fileName = 'tests/data/Reader/XLS/bug-pr-3734.xls';
+        $spreadsheet = IOFactory::load($fileName);
+        $sheet = $spreadsheet->getActiveSheet();
+        self::assertSame('Calibri', $sheet->getStyle('A1')->getFont()->getName());
+        $spreadsheet->disconnectWorksheets();
+    }
+}
diff --git a/tests/data/Reader/XLS/bug-pr-3734.xls b/tests/data/Reader/XLS/bug-pr-3734.xls
new file mode 100644
index 000000000..8fa0e56a3
Binary files /dev/null and b/tests/data/Reader/XLS/bug-pr-3734.xls differ