// Define a wrapper class to hold the JSON data
public class AccountContactWrapper {
    public String AccountName;
    public String Desc;
    public String Phone;
    public String ContactLastName;
}

// Parse the JSON data and create an Account and Contact for each object
String jsonString = '[{"AccountName":"Test Account new","Desc":"Test Desc","Phone":"9898989898","ContactLastName":"Test contact"}]';
List<AccountContactWrapper> accountContactList = (List<AccountContactWrapper>) JSON.deserialize(jsonString, List<AccountContactWrapper>.class);

List<Account> accountList = new List<Account>();
List<Contact> contactList = new List<Contact>();
for (AccountContactWrapper acw : accountContactList) {
    // Create a new Account and populate its fields
    Account account = new Account();
    account.Name = acw.AccountName;
    account.Description = acw.Desc;
    account.Phone = acw.Phone;
    accountList.add(account);

    // Create a new Contact and populate its fields
    Contact contact = new Contact();
    contact.LastName = acw.ContactLastName;
    contact.AccountId = account.Id;
    contactList.add(contact);
}

// Insert the new Account and Contact records
insert accountList;
insert contactList;