Psychology Today has a short interview with psychologist Leslie Becker-Phelps, author of Insecure in Love:

Winch: Can you really change your attachment style? And if you can, how?

Becker-Phelps: You most definitely can change. However, keep in mind that you are changing something fundamental in yourself, so doing so will take time and patience.

You need to begin by paying attention to your insecure patterns. As you observe them, you will gain more clarity about them. For instance, you might notice that you tend to feel inadequate and often harshly criticize yourself. Once you see such patterns, you can begin to question them. One good way to do this with self-criticism is to ask yourself how you would respond to a friend in the same situation. Frequently, the answer is that you would be much more compassionate.

Finally, you can practice this compassionate response with yourself. Because changing your attachment style is so difficult, it is very beneficial to be compassionate toward your struggles. It can help motivate you toward happier relationships with yourself and others, and to support yourself when things don’t go well. Although self-compassion can be difficult to learn, it also has the power to help you heal and change.

More on Attachment and Personality Types:

What Attachment Type Are You?
Type: Secure
Type: Anxious-Preoccupied
Type: Dismissive-Avoidant
Type: Fearful-Avoidant (aka Anxious-Avoidant)
Avoidant: Emotions Repressed Beneath Conscious Level
Serial Monogamy: the Fearful-Avoidant Do It Faster
Anxious-Preoccupied: Stuck on the Dismissive?
Anxious-Preoccupied / Dismissive-Avoidant Couples: the Silent Treatment
nxious-Preoccupied: Clingy and Insecure Relationship Example
Domestic Violence: Ray and Janay Rice
Malignant Narcissists
Teaching Narcissists to Activate Empathy
Histrionic Personality: Seductive, Dramatic, Theatrical
Life Is Unfair! The Great Chain of Dysfunction Ends With You.
Love Songs of the Secure Attachment Type
On Addiction and the Urge to Rescue
Sale! Sale! Sale! – “Bad Boyfriends” for Kindle, $2.99
Controlling Your Inner Critic: Subpersonalities
“Big Bang Theory” — Aspergers and Emotional/Social Intelligence
Porn Addiction and NoFAP
Introverts in Management