diff --git a/NEWS.md b/NEWS.md
index daa8151518..9f182939be 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -60,6 +60,8 @@
 
 13. `rbindlist()` (and therefore the `rbind()` method for `data.table`s) no longer raises an error upon encountering more than approximately 50000 columns in a list entry, [#7793](https://github.com/Rdatatable/data.table/issues/7793). The bug was introduced in `data.table` version 1.18.2.1. Thanks to @rickhelmus for the report and @aitap for the fix.
 
+14. `print.data.table()` now correctly displays data when `col.names="none"` and `row.names=FALSE`, [#7735](https://github.com/Rdatatable/data.table/issues/7735). Previously, the output was entirely suppressed because the internal logic relied on row markers (e.g., `1:`) to identify data lines. Thanks to @jan-swissre for the report and @YourGitHubHandle for the fix.
+
 ### Notes
 
 1. {data.table} now depends on R 3.5.0 (2018).
diff --git a/R/print.data.table.R b/R/print.data.table.R
index e602f80d69..e9baf7a78e 100644
--- a/R/print.data.table.R
+++ b/R/print.data.table.R
@@ -131,7 +131,14 @@ print.data.table = function(x, topn=getOption("datatable.print.topn"),
     trunc.cols = length(not_printed) > 0L
   }
   print_default = function(x) {
-    if (col.names != "none") cut_colnames = identity
+    if (col.names != "none") {
+      cut_colnames = identity
+    } else if (isFALSE(row.names)) {
+      cut_colnames = function(x) {
+        out = capture.output(x)
+        if (length(out) > 0L) writeLines(out[-1L])
+      }
+    }
     cut_colnames(print(x, right=TRUE, quote=quote, na.print=na.print))
     # prints names of variables not shown in the print
     if (trunc.cols) trunc_cols_message(not_printed, abbs, class, col.names)
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 80df54b6aa..3edb7aceca 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -21775,3 +21775,8 @@ test(2377.44, copy(dt)[!(a < 5 & b != "d"), .ROW := NULL], dt[1:3])
 dt = data.table(a=1:3)
 test(2377.91, truelength(dt$a), 0L)
 test(2377.92, {setallocrow(dt); truelength(dt$a)}, 3L)
+
+# #7735 col.names="none" should suppress only column headers, not data
+test(2378.1, print(data.table(c1=1:2, c2=letters[1:2]), nrows=Inf, class=FALSE, row.names=FALSE, show.indices=FALSE, print_keys=FALSE, col.names="none"), output=" 1 a\n 2 b")
+test(2378.2, print(data.table(x=1:3), class=FALSE, row.names=FALSE, col.names="none"), output=" 1\n 2\n 3")
+test(2378.3, print(data.table(c1=1:3, c2=letters[1:3]), row.names=TRUE, class=FALSE, col.names="none"), output="1: 1 a\n2: 2 b\n3: 3 c")