diff --git src/wp-includes/general-template.php src/wp-includes/general-template.php
index f9a529f..6ed5151 100644
--- src/wp-includes/general-template.php
+++ src/wp-includes/general-template.php
@@ -2659,12 +2659,21 @@ function paginate_links( $args = '' ) {
 	// Merge additional query vars found in the original URL into 'add_args' array.
 	if ( isset( $url_parts[1] ) ) {
 		// Find the format argument.
-		$format_query = parse_url( str_replace( '%_%', $args['format'], $args['base'] ), PHP_URL_QUERY );
-		wp_parse_str( $format_query, $format_arg );
+		$format = explode( '?', str_replace( '%_%', $args['format'], $args['base'] ) );
+		$format_query = isset( $format[1] ) ? $format[1] : '';
+		wp_parse_str( $format_query, $format_args );
+
+		// Find the query args of the requested URL.
+		wp_parse_str( $url_parts[1], $url_query_args );
 
 		// Remove the format argument from the array of query arguments, to avoid overwriting custom format.
-		wp_parse_str( remove_query_arg( array_keys( $format_arg ), $url_parts[1] ), $query_args );
-		$args['add_args'] = array_merge( $args['add_args'], urlencode_deep( $query_args ) );
+		foreach ( $format_args as $format_arg => $format_arg_value ) {
+			if ( isset( $url_query_args[ $format_arg ] ) ) {
+				unset( $url_query_args[ $format_arg ] );
+			}
+		}
+
+		$args['add_args'] = array_merge( $args['add_args'], urlencode_deep( $url_query_args ) );
 	}
 
 	// Who knows what else people pass in $args
diff --git tests/phpunit/tests/general/paginateLinks.php tests/phpunit/tests/general/paginateLinks.php
index b6c1a32..ba0b77b 100644
--- tests/phpunit/tests/general/paginateLinks.php
+++ tests/phpunit/tests/general/paginateLinks.php
@@ -311,4 +311,24 @@ EXPECTED;
 
 		$this->assertContains( "<span class='page-numbers current'>3</span>", $links );
 	}
+
+	/**
+	 * @ticket 31939
+	 */
+	public function test_custom_base_query_arg_should_be_stripped_from_current_url_before_generating_pag_links() {
+		// Fake the current URL: example.com?foo
+		$request_uri = $_SERVER['REQUEST_URI'];
+		$_SERVER['REQUEST_URI'] = add_query_arg( 'foo', '', $request_uri );
+
+		$links = paginate_links( array(
+			'base'    => add_query_arg( 'foo', '%_%', home_url() ),
+			'format'  => '%#%',
+			'total'   => 5,
+			'current' => 1,
+			'type'    => 'array',
+		) );
+
+		$page_2_url = home_url() . '?foo=2';
+		$this->assertContains( "<a class='page-numbers' href='$page_2_url'>2</a>", $links );
+	}
 }