diff --git a/lib/datasets/math_base_funcs.py b/lib/datasets/math_base_funcs.py
index 42a4bd4..a77634b 100644
--- a/lib/datasets/math_base_funcs.py
+++ b/lib/datasets/math_base_funcs.py
@@ -103,11 +103,32 @@ class FitFunc(abc.ABC):
         )
 
 
+class LinearFunc(FitFunc):
+    """The linear function that outputs f(x) = a * x + b."""
+
+    def __init__(self, list_of_points=None, params=None):
+        super(LinearFunc, self).__init__(2, list_of_points, params)
+
+    def __call__(self, x):
+        self.check_valid()
+        return self._params[0] * x + self._params[1]
+
+    def _getitem(self, x, weights):
+        return weights[0] * x + weights[1]
+
+    def __repr__(self):
+        return "{name}({a} * x + {b})".format(
+            name=self.__class__.__name__,
+            a=self._params[0],
+            b=self._params[1],
+        )
+
+
 class QuadraticFunc(FitFunc):
     """The quadratic function that outputs f(x) = a * x^2 + b * x + c."""
 
-    def __init__(self, list_of_points=None):
-        super(QuadraticFunc, self).__init__(3, list_of_points)
+    def __init__(self, list_of_points=None, params=None):
+        super(QuadraticFunc, self).__init__(3, list_of_points, params)
 
     def __call__(self, x):
         self.check_valid()
diff --git a/lib/datasets/math_core.py b/lib/datasets/math_core.py
index 6b12d88..5dd2429 100644
--- a/lib/datasets/math_core.py
+++ b/lib/datasets/math_core.py
@@ -1,7 +1,7 @@
 #####################################################
 # Copyright (c) Xuanyi Dong [GitHub D-X-Y], 2021.05 #
 #####################################################
-from .math_base_funcs import QuadraticFunc, CubicFunc, QuarticFunc
+from .math_base_funcs import LinearFunc, QuadraticFunc, CubicFunc, QuarticFunc
 from .math_dynamic_funcs import DynamicLinearFunc
 from .math_dynamic_funcs import DynamicQuadraticFunc
 from .math_adv_funcs import ConstantFunc
diff --git a/lib/datasets/synthetic_core.py b/lib/datasets/synthetic_core.py
index f05024b..9d05d7a 100644
--- a/lib/datasets/synthetic_core.py
+++ b/lib/datasets/synthetic_core.py
@@ -3,9 +3,10 @@
 #####################################################
 from .synthetic_utils import TimeStamp
 from .synthetic_env import SyntheticDEnv
-from .math_dynamic_funcs import DynamicLinearFunc
-from .math_dynamic_funcs import DynamicQuadraticFunc
-from .math_adv_funcs import ConstantFunc, ComposedSinFunc
+from .math_core import LinearFunc
+from .math_core import DynamicLinearFunc
+from .math_core import DynamicQuadraticFunc
+from .math_core import ConstantFunc, ComposedSinFunc
 
 
 __all__ = ["TimeStamp", "SyntheticDEnv", "get_synthetic_env"]
@@ -32,7 +33,8 @@ def get_synthetic_env(total_timestamp=1000, num_per_task=1000, mode=None, versio
         function = DynamicLinearFunc()
         function_param = dict()
         function_param[0] = ComposedSinFunc(
-            amplitude_scale=ConstantFunc(1.0), period_phase_shift=ConstantFunc(10)
+            amplitude_scale=ConstantFunc(1.0),
+            period_phase_shift=LinearFunc(params={0: 10, 1: 0}),
         )
         function_param[1] = ConstantFunc(constant=0.9)
     elif version == "v2":