With introduction of smart things into our lives, cloud computing is used in many different areas and changes the communication method. However, cloud computing should guarantee the complete security assurance in terms of privacy protection, confidentiality, and integrity. In this paper, a Homomorphic Encryption Scheme based on Elliptic Curve Cryptography (HES-ECC) is proposed for secure data transfer and storage. The scheme stores the data in the cloud after encrypting them. While calculations, such as addition or multiplication, are applied to encrypted data on cloud, these calculations are transmitted to the original data without any decryption process. Thus, the cloud server has only ability of accessing the encrypted data for performing the required computations and for fulfilling requested actions by the user. Hence, storage and transmission security of data are ensured. The proposed public key HES-ECC is designed using modified Weil-pairing for encryption and additional homomorphic property. HES-ECC also uses bilinear pairing for multiplicative homomorphic property. Security of encryption scheme and its homomorphic aspects are based on the hardness of Elliptic Curve Discrete Logarithm Problem (ECDLP), Weil Diffie-Hellman Problem (WDHP), and Bilinear Diffie-Helman Problem (BDHP).