diff --git a/scipy/integrate/_ivp/ivp.py b/scipy/integrate/_ivp/ivp.py
index b91929f9b91e..be47b1190c3e 100644
--- a/scipy/integrate/_ivp/ivp.py
+++ b/scipy/integrate/_ivp/ivp.py
@@ -456,6 +456,10 @@ def solve_ivp(fun, t_span, y0, method='RK45', t_eval=None, dense_output=False,
     if t_eval is None:
         ts = [t0]
         ys = [y0]
+    elif t_eval is not None and dense_output:
+        ts = []
+        ti = [t0]
+        ys = []
     else:
         ts = []
         ys = []
@@ -531,6 +535,9 @@ def solve_ivp(fun, t_span, y0, method='RK45', t_eval=None, dense_output=False,
                 ts.append(t_eval_step)
                 ys.append(sol(t_eval_step))
                 t_eval_i = t_eval_i_new
+        
+        if t_eval is not None and dense_output:
+            ti.append(t)
 
     message = MESSAGES.get(status, message)
 
@@ -545,7 +552,10 @@ def solve_ivp(fun, t_span, y0, method='RK45', t_eval=None, dense_output=False,
         ys = np.hstack(ys)
 
     if dense_output:
-        sol = OdeSolution(ts, interpolants)
+        if t_eval is None:
+            sol = OdeSolution(ts, interpolants)
+        else:
+            sol = OdeSolution(ti, interpolants)
     else:
         sol = None
 
diff --git a/scipy/integrate/tests/test_ivp.py b/scipy/integrate/tests/test_ivp.py
index cb7729654f2d..e7f174596fbe 100644
--- a/scipy/integrate/tests/test_ivp.py
+++ b/scipy/integrate/tests/test_ivp.py
@@ -518,6 +518,33 @@ def test_t_eval():
                   rtol=rtol, atol=atol, t_eval=t_eval)
 
 
+def test_t_eval_dense_output():
+    rtol = 1e-3
+    atol = 1e-6
+    y0 = [1/3, 2/9]
+    t_span = [5, 9]
+    t_eval = np.linspace(t_span[0], t_span[1], 10)
+    res = solve_ivp(fun_rational, t_span, y0, rtol=rtol, atol=atol,
+                    t_eval=t_eval)
+    res_d = solve_ivp(fun_rational, t_span, y0, rtol=rtol, atol=atol,
+                      t_eval=t_eval, dense_output=True)
+    assert_equal(res.t, t_eval)
+    assert_(res.t_events is None)
+    assert_(res.success)
+    assert_equal(res.status, 0)
+
+    assert_equal(res.t, res_d.t)
+    assert_equal(res.y, res_d.y)
+    assert_(res_d.t_events is None)
+    assert_(res_d.success)
+    assert_equal(res_d.status, 0)
+
+    # if t and y are equal only test values for one case
+    y_true = sol_rational(res.t)
+    e = compute_error(res.y, y_true, rtol, atol)
+    assert_(np.all(e < 5))
+
+
 def test_no_integration():
     for method in ['RK23', 'RK45', 'Radau', 'BDF', 'LSODA']:
         sol = solve_ivp(lambda t, y: -y, [4, 4], [2, 3],