diff --git a/src/core/src/pass/visualize_tree.cpp b/src/core/src/pass/visualize_tree.cpp
index a0d0b4a05e3094..cf7bb6e85bdf37 100644
--- a/src/core/src/pass/visualize_tree.cpp
+++ b/src/core/src/pass/visualize_tree.cpp
@@ -540,15 +540,7 @@ std::string ov::pass::VisualizeTree::get_constant_value(std::shared_ptr<Node> no
     ss << pretty_partial_shape(node->get_output_partial_shape(0), m_symbol_to_name);
 
     if (const auto& constant = ov::as_type_ptr<ov::op::v0::Constant>(node)) {
-        std::string value;
-        try {
-            value = get_value(constant, max_elements);
-        } catch (ov::AssertFailure& ex) {
-            value = std::string("ov::AssertFailure: ") + ex.what();
-        } catch (std::exception& ex) {
-            value = ex.what();
-        }
-        ss << "\nvalue: " << value;
+        ss << "\nvalue: " << get_value(constant, max_elements);
     }
     return ss.str();
 }
diff --git a/src/core/tests/pass/visualize_tree.cpp b/src/core/tests/pass/visualize_tree.cpp
new file mode 100644
index 00000000000000..1b21f2b294e3db
--- /dev/null
+++ b/src/core/tests/pass/visualize_tree.cpp
@@ -0,0 +1,66 @@
+// Copyright (C) 2018-2024 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+//
+
+#include "openvino/pass/visualize_tree.hpp"
+
+#include "common_test_utils/file_utils.hpp"
+#include "common_test_utils/test_assertions.hpp"
+#include "openvino/core/model.hpp"
+#include "openvino/op/add.hpp"
+#include "openvino/op/constant.hpp"
+
+namespace ov {
+namespace test {
+
+using ov::op::v0::Constant;
+using ov::op::v0::Parameter;
+using ov::op::v0::Result;
+using ov::op::v1::Add;
+
+class VisualizeTreeTest : public testing::Test {
+protected:
+    void TearDown() override {
+        if (util::file_exists(vt_svg_file_path)) {
+            std::remove(vt_svg_file_path.c_str());
+        }
+
+        if (util::file_exists(dot_file_path)) {
+            std::remove(dot_file_path.c_str());
+        }
+    }
+
+    static std::shared_ptr<Model> make_dummy_add_model(const element::Type& precision) {
+        const auto c = Constant::create(precision, Shape{3}, {1.0f, -23.21f, std::numeric_limits<float>::infinity()});
+        const auto input = std::make_shared<Parameter>(precision, Shape{});
+        const auto add = std::make_shared<Add>(c, input);
+        const auto output = std::make_shared<Result>(add);
+        return std::make_shared<Model>(ResultVector{output}, ParameterVector{input});
+    }
+
+    const std::string vt_svg_file_path =
+        util::path_join({utils::getExecutableDirectory(), utils::generateTestFilePrefix() + "_tree.svg"});
+    const std::string dot_file_path = vt_svg_file_path + ".dot";
+};
+
+TEST_F(VisualizeTreeTest, model_has_constant_with_inf) {
+    constexpr auto precision = element::f32;
+    const auto model = make_dummy_add_model(precision);
+
+    pass::VisualizeTree vt(vt_svg_file_path);
+
+    OV_ASSERT_NO_THROW(vt.run_on_model(model));
+    ASSERT_TRUE(util::file_exists(dot_file_path)) << dot_file_path;
+}
+
+TEST_F(VisualizeTreeTest, model_has_constant_with_no_inf) {
+    constexpr auto precision = element::f16;
+    const auto model = make_dummy_add_model(precision);
+
+    pass::VisualizeTree vt(vt_svg_file_path);
+
+    OV_ASSERT_NO_THROW(vt.run_on_model(model));
+    ASSERT_TRUE(util::file_exists(dot_file_path)) << dot_file_path;
+}
+}  // namespace test
+}  // namespace ov