diff --git a/neural_network/activation_functions/gaussian_error_linear_unit.py b/neural_network/activation_functions/gaussian_error_linear_unit.py
new file mode 100644
index 000000000000..ced582972990
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+++ b/neural_network/activation_functions/gaussian_error_linear_unit.py
@@ -0,0 +1,38 @@
+"""
+Gaussian Error Linear Unit (GELU)
+
+Use Case: GELU permits negative inputs for enhanced backprop gradients.
+For more detailed information, you can refer to the following link:
+https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Gaussian-error_linear_unit_(GELU)
+"""
+
+import numpy as np
+from scipy.special import erf
+
+
+def gaussian_error_linear_unit(vector: np.ndarray) -> np.ndarray:
+    """
+         Implements the GELU activation function.
+         Parameters:
+             vector: the array containing input of gelu activation
+         return:
+         gelu (np.array): The input numpy array after applying gelu.
+
+    Examples:
+    >>> gaussian_error_linear_unit(vector=np.array([-1.1, 2.3, -3.4, 4.5]))
+    array([-1.49232667e-01,  2.30000000e+00, -1.14555950e-03,  4.50000000e+00])
+
+    >>> gaussian_error_linear_unit(vector=np.array([-9.2,-0.3,0.45,-4.56]))
+    array([-0.00000000e+00, -1.14626573e-01,  4.50000000e-01, -1.16630255e-05])
+
+
+    """
+    return np.where(
+        vector > 0, vector, (vector * 0.5 * (1.0 + erf(vector / np.sqrt(2.0))))
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()