Yes, there are a few different ways of getting around this issue.
Depending on factors like the seriousness, frequency and time since the crimes were committed, your present behaviour and the likelihood of you reoffending, your representative can make convincing legal arguments, informed and backed by legal precedents, that you should be “deemed rehabilitated” (if applicable) or your criminal record should not prevent you from entering Canada depending on the circumstances of your specific case and the reasons why you wish to enter Canada.
Alternatively, you may apply for a “Temporary Resident Permit” which allows you to temporarily enter Canada based on compassionate grounds despite being inadmissible. This is a discretionary permit and issued by an officer if he/she is convinced that you deserve to enter Canada temporarily and believes that you will leave at the expiration of the permit.
For more details on these and other methods to deal with criminal records in immigration matters, you should consult an experienced representative in Canadian Immigration Law.